{"id":2406,"date":"2011-03-12T17:57:40","date_gmt":"2011-03-12T09:57:40","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=2406"},"modified":"2011-03-12T18:15:39","modified_gmt":"2011-03-12T10:15:39","slug":"%e5%9c%a3%e6%af%8d%e7%8e%9b%e4%b8%bd%e4%ba%9a%e7%9a%84smoluchowski","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/2406","title":{"rendered":"\u5723\u6bcd\u739b\u4e3d\u4e9a\u7684Smoluchowski"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"2406\">\n<h3>\u5723\u6bcd\u739b\u4e3d\u4e9a\u7684Smoluchowski<\/h3>\n<div id=\"attachment_2443\" style=\"width: 310px\" class=\"wp-caption alignleft\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2.jpeg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2443\" data-attachment-id=\"2443\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/2406\/smoluchowski_2\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2.jpeg\" data-orig-size=\"351,326\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"M. Smoluchowski\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;M. Smoluchowski&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2.jpeg\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2-300x278.jpg\" alt=\"M. Smoluchowski\" title=\"M. Smoluchowski\" width=\"300\" height=\"278\" class=\"size-medium wp-image-2443\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2-300x278.jpg 300w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2.jpeg 351w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><p id=\"caption-attachment-2443\" class=\"wp-caption-text\">M. Smoluchowski<\/p><\/div>\n<p>\u6700\u8fd1\u5728\u5b66\u4e60Smoluchowski\u7684coagulation\u7406\u8bba\u3002\u4e0aGoogle\u641c\u7d22\u201cSmoluchowski\u7406\u8bba\u201d\uff0c\u7b2c\u4e00\u4e2a\u641c\u7d22\u7ed3\u679c\u7684\u6807\u9898\u4e3a<a href=\"http:\/\/www.worldlingo.com\/ma\/enwiki\/zh_cn\/Marian_Smoluchowski\">\u201c\u5723\u6bcd\u739b\u4e3d\u4e9a\u7684Smoluchowski\u201d<\/a>\u3002\u539f\u6765\u662f\u81ea\u52a8\u7ffb\u8bd1\u8f6f\u4ef6\u5f04\u7684\uff0c\u628aSmoluchowski\u7684first name\u7ed9\u8bd1\u8fc7\u6765\u4e86\u3002\u6309\u7406\u4e5f\u6ca1\u9519\u3002\u8bf4\u4e0d\u5b9aSmoluchowski\u7684\u7236\u6bcd\u7ed9\u8fd9\u5b69\u5b50\u9009\u62e9\u8fd9\u4e2a\u540d\u5b57\u5c31\u662f\u5e0c\u671b\u5b83\u80fd\u50cf\u5723\u6bcd\u7684\u5b69\u5b50\u90a3\u6837blessed\u3002<\/p>\n<h3>\u5173\u4e8e\u5982\u4f55\u901a\u8fc7\u52a8\u6001\u5149\u6563\u5c04\u6d4bpotential barrier<\/h3>\n<p>\u6211\u4e4b\u6240\u4ee5\u8981\u770bSmoluchowski\u7406\u8bba\uff0c\u662f\u7531\u4e8e\u9047\u5230\u4e86\u4e00\u4e9b\u6587\u7ae0\u901a\u8fc7\u52a8\u6001\u5149\u6563\u5c04\uff08DLS\uff09\u6765\u83b7\u5f97\u7c92\u5b50\u95f4\u7684pair potential\u7684\u90a3\u4e2a\u6240\u8c13primary maximum\uff0c\u6216\u8005\u8bf4potential barrier\uff08<i>U<\/i><sub>max<\/sub>\uff09\u3002DLS\u53ef\u4ee5\u7528\u6765\u6d4b\u5e73\u5747\u6269\u6563\u7cfb\u6570<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\bar{D}\" title=\"\\bar{D}\" \/>\u3002\u5982\u679c\u6837\u54c1\u968f\u65f6\u95f4\u4e0d\u65ad\u53d1\u751faggrigation\uff0c\u90a3\u4e48\u5e73\u5747\u6269\u6563\u7cfb\u6570\u5c31\u4f1a\u968f\u65f6\u95f4\u53d8\u5316\uff0c\u6d4b\u51fa<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\bar{D}\\left ( t \\right )\" title=\"\\bar{D}\\left ( t \\right )\" \/>\u3002Pusey\u7b49\uff08J. Chem. Phys. 1982, 77, 4270\uff09\u7ed9\u51fa\u4e86\u7ed9\u5b9a\u5c3a\u5bf8\u5206\u5e03\u7684\u7c92\u5b50\u4f53\u7cfb\u7684\u5e73\u5747\u6269\u6563\u7cfb\u6570\u8868\u8fbe\u5f0f\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\bar{D}_{0}=\\frac{\\sum_{p}N_{p}f_{p}^{2}D_{0,p}}{\\sum_{p}N_{p}f_{p}^{2}}\" title=\"\\bar{D}_{0}=\\frac{\\sum_{p}N_{p}f_{p}^{2}D_{0,p}}{\\sum_{p}N_{p}f_{p}^{2}}\" \/><\/p>\n<p>\u5176\u4e2d\u4e0b\u6807<i>p<\/i>\u662f\u6307\u7b2c<i>p<\/i>\u79cd\u5c3a\u5bf8\u3002<i>N<\/i>\u662f\u4e2a\u6570\uff0c<i>f<\/i>\u662f\u6563\u5c04\u5f3a\u5ea6\u3002\u5bf9\u4e8e\u5c3a\u5bf8\u5206\u5e03\u672c\u6765\u662f\u5355\u5206\u6563\u7684\u7c92\u5b50\uff0c\u5728\u805a\u96c6\u8fc7\u7a0b\u4e2d\u5c31\u4f1a\u6709\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u5230<i>p<\/i>\u805a\u4f53\u7b49\u5927\u5c0f\u4e0d\u4e00\u7684\u5355\u5143\u5b58\u5728\uff0c\u56e0\u6b64\u662f\u4e00\u4e2a\u591a\u5206\u6563\u4f53\u7cfb\uff0c\u9002\u7528Pusey\u7684\u5f0f\u5b50\u3002\u800c\u4e14\u5404<i>p<\/i>\u805a\u4f53\u7684\u6570\u91cf\u90fd\u968f\u65f6\u95f4\u53d8\u5316\uff0c\u5373\u6574\u4e2a\u5c3a\u5bf8\u5206\u5e03\u5728\u968f\u65f6\u95f4\u53d8\u5316\u3002\u56e0\u6b64Pusey\u7684\u90a3\u6761\u5f0f\u5b50\u5c31\u8981\u52a0\u4e0a\u65f6\u95f4\u4f9d\u8d56\u6027\uff0c\u53d8\u6210\u4e86\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\bar{D}_{0}\\left(t \\right )=\\frac{\\sum_{p}N_{p}\\left(t \\right )f_{p}^{2}D_{0,p}}{\\sum_{p}N_{p}\\left(t \\right )f_{p}^{2}}\" title=\"\\bar{D}_{0}\\left(t \\right )=\\frac{\\sum_{p}N_{p}\\left(t \\right )f_{p}^{2}D_{0,p}}{\\sum_{p}N_{p}\\left(t \\right )f_{p}^{2}}\" \/><\/p>\n<p>Versmold &amp; H&auml;rtl\uff08J. Chem. Phys. 1983, 79, 4006\uff09\u901a\u8fc7\u7b80\u5355\u5047\u8bbe\u5404<i>p<\/i>\u805a\u4f53\u90fd\u662f\u7403\u4f53\uff0c\u4ee5\u4fbf\u90a3\u4e2a\u6269\u6563\u7cfb\u6570\u4e0e\u5c3a\u5bf8\u7684\u5173\u7cfb\u5f0f\u80fd\u5e94\u7528\u5728\u5404\u4e2a<i>p<\/i>\u805a\u4f53\u4e0a\uff1b\u53e6\u6839\u636e\u5149\u6563\u5c04\u539f\u7406\uff0c\u6563\u5c04\u5f3a\u5ea6<i>f<\/i>\u8ddf\u7c92\u5b50\u4f53\u79ef\uff08\u534a\u5f84\u7684\u7acb\u65b9\uff09\u6709\u5173\u3002\u8fd9\u6837\u5c31\u628aPusey\u7684\u5f0f\u5b50\u4e2d<i>f<\/i><sup>p<\/sup>\u548c<i>D<\/i><sub>0,p<\/sub>\u76f4\u63a5\u7528<i>a<\/i><sub>p<\/sub>\u4ee3\u66ff\u4e86\uff0c\u53d8\u6210\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\overline{D_{0}}\\left(t \\right )=\\frac{k T\\sum_{p}N_{p}\\left(t \\right )a_{p}^{5}}{6\\pi\\eta\\sum_{p}N_{p}\\left(t \\right )a_{p}^{6}} =\\frac{k T\\overline{a_{p}^{5}}\\left(t \\right )}{6\\pi\\eta\\overline{a_{p}^{6}}\\left(t \\right )}=D_{0}\\frac{\\overline{p^{\\frac{5}{3}}}\\left(t \\right )}{\\overline{p^{\\frac{6}{3}}}\\left(t \\right )}\" title=\"\\overline{D_{0}}\\left(t \\right )=\\frac{k T\\sum_{p}N_{p}\\left(t \\right )a_{p}^{5}}{6\\pi\\eta\\sum_{p}N_{p}\\left(t \\right )a_{p}^{6}} =\\frac{k T\\overline{a_{p}^{5}}\\left(t \\right )}{6\\pi\\eta\\overline{a_{p}^{6}}\\left(t \\right )}=D_{0}\\frac{\\overline{p^{\\frac{5}{3}}}\\left(t \\right )}{\\overline{p^{\\frac{6}{3}}}\\left(t \\right )}\" \/><\/p>\n<p>Smoluchowski\u65b9\u7a0b<i>N<\/i><sub>p<\/sub>(<i>t<\/i>\/<i>t<\/i><sub>1\/2<\/sub>)=&#8230;\u7684\u7528\u5904\u5c31\u662f\u7528\u6765\u7b97\u4e0a\u5f0f\u90a3\u4e24\u4e2a<i>p<\/i>\u7684\u77e9\u3002\u636eVersmold &amp; H&auml;rtl\u7684\u6587\u7ae0\u6240\u5f15\u8ff0\uff0c<i>p<\/i>\u7684\u5747\u65b9\u503c\uff086\/3\uff09\u4e4b\u524d\u6709\u4eba\u7ed9\u51fa\u89e3\u6790\u89e3\u4e86\u3002\u53ef\u8fd95\/3\u9636\u77e9\u53ef\u600e\u4e48\u529e\u5462\uff1fVersmold &amp; H&auml;rtl\u53ea\u80fd\u5728\u65f6\u95f4<i>t<\/i>\/<i>t<\/i><sub>1\/2<\/sub>\u5f88\u5c0f\u7684\u6761\u4ef6\u4e0b\uff08\u5373aggregation\u521a\u53d1\u751f\u6ca1\u591a\u4e45\uff09\u628aSmoluchowski\u65b9\u7a0b\u7ed9\u5c55\u5f00\u4e86\u53d6\u8fd1\u4f3c\uff0c\u8fd9\u6837\u7684\u8bdd<i>p<\/i>\u7684<i>n<\/i>\/3\u9636\u77e9\u968f<i>t<\/i>\/<i>t<\/i><sub>1\/2<\/sub>\u7684\u53d8\u5316\u5c31\u90fd\u80fd\u8ba1\u7b97\u3002\u4e0d\u8fc7\u8fd9\u6837\u7ed9\u51fa\u7684\u8868\u8fbe\u5f0f\u662f\u4e2a\u7ebf\u6027\u5f0f\uff0c\u53ea\u9002\u7528\u4e8e\u805a\u96c6\u53cd\u5e94\u7684\u521d\u671f\u3002\u81f3\u4e8e\u9002\u7528\u4e8e\u6574\u4e2a\u65f6\u95f4\u57df\u7684\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u7528\u8ba1\u7b97\u673a\u7ed9\u51fa\u6570\u503c\u89e3\u3002<\/p>\n<p>\u4ee5\u4e0a\u7684\u5de5\u4f5c\uff0c\u901a\u8fc7Smoluchowski\u65b9\u7a0b\uff0c\u7ed9\u51fa\u4e86\u7c92\u5b50\u4f53\u7cfb\u5728\u805a\u96c6\u8fc7\u7a0b\u4e2d\u6269\u6563\u7cfb\u6570\u7684\u65f6\u95f4\u4f9d\u901f\u5173\u7cfb<i>D<\/i>(<i>t<\/i>)\u7684\u8868\u8fbe\u5f0f\uff0c\u5f0f\u4e2d\u552f\u4e00\u7684\u53c2\u6570\u662f\u90a3\u4e2a<i>t<\/i><sub>1\/2<\/sub>\uff0c\u6240\u4ee5\uff0c\u62ff\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u53bb\u62df\u5408\u5b9e\u6d4b\u6570\u636e\uff0c\u5c31\u80fd\u5f97\u5230\u8fd9\u4e2a<i>t<\/i><sub>1\/2<\/sub>\u4e86\u3002\u8fd9\u4e2a<i>t<\/i><sub>1\/2<\/sub>\u8ddf\u805a\u96c6\u53cd\u5e94\u7684\u901f\u7387\u5e38\u6570<i>k<\/i>\u76f4\u63a5\u6709\u5173\uff1a<i>k<\/i>=1\/(<i>t<\/i><sub>1\/2<\/sub><i>N<\/i><sub>0<\/sub>)\uff0c\u5176\u4e2d<i>N<\/i><sub>0<\/sub>\u662f\u6700\u521d\u7684\u7c92\u5b50\u5bc6\u5ea6\uff08\u4e2a\u6570\u6bd4\u4f53\u79ef\uff09\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u7528\u52a8\u6001\u5149\u6563\u5c04\u53ef\u4ee5\u6d4b\u51fa<i>k<\/i>\u3002<\/p>\n<p><i>k<\/i>\u53c8\u8ddf\u7c92\u5b50\u95f4\u7684pair potential\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u9996\u5148\uff0c\u8fd9\u4e2a\u901f\u7387\u5e38\u6570\u662f\u805a\u96c6\u53cd\u5e94\u7684\u6570\u7387\u5e38\u6570\uff0c\u4e24\u4e2a\u7c92\u5b50\u78b0\u649e\u540e\u8981\u53d1\u751f\u805a\u96c6\uff0c\u5b83\u4eec\u5f53\u7136\u8981\u514b\u670d\u6389\u4e24\u8005\u95f4\u7684potential barrier\u3002\u56e0\u6b64\u7c92\u5b50\u95f4\u7684potential barrier\u5c31\u51b3\u5b9a\u4e86\u6709\u6548\u78b0\u649e\u5360\u603b\u78b0\u649e\u6570\u4e4b\u6bd4\u4f8b\u3002\u603b\u78b0\u649e\u6570\u65e0\u975e\u5c31\u662f\u5e03\u6717\u8fd0\u52a8\u51b3\u5b9a\uff08\u7c98\u5ea6\u3001\u5c3a\u5bf8\u90fd\u5b9a\u4e86\u8fd9\u4e2a\u5c31\u662f\u5b9a\u7684\uff09\u3002\u56e0\u6b64\uff0c\u90a3\u4e2a\u6bd4\u4f8b\u2014\u2014\u79f0\u4e3astability ratio\uff0c<i>W<\/i>\u2014\u2014\u5c31\u8ddfpotential barrier\u76f4\u63a5\u6709\u5173\u4e86\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?W=2 a\\int_{2a}^{\\infty}\\exp \\left[\\frac{U\\left(r \\right )}{k T} \\right ]r^{-2} d r\" title=\"W=2 a\\int_{2a}^{\\infty}\\exp \\left[\\frac{U\\left(r \\right )}{k T} \\right ]r^{-2} d r\" \/><\/p>\n<p>\u636e\u4f20\u4e0a\u5f0f\u662fN. Fuch\u7ed9\u7684\uff0c\u4e4b\u6240\u4ee5\u8bf4\u201c\u636e\u4f20\u201d\uff0c\u662f\u56e0\u4e3a\u6211\u81ea\u5df1\u6ca1\u6709\u770b\u8fc7N. Fuch\u7684\u8bba\u6587\uff08\uff09\u2014\u2014\u5fb7\u8bed\u7684\uff0c\u770b\u4e0d\u61c2\u3002\u6211\u53ea\u77e5\u9053\u5f88\u591a\u4eba\u4e00\u63d0\u5230stability ratio\uff0c\u5c31\u5f15N. Fuch\u8fd9\u7bc7\u4e1c\u897f\u3002<\/p>\n<p>\u79ef\u5206\u5f0f\u4e2d\u7684<i>U<\/i>(<i>r<\/i>)\u5f62\u5f0f\u4e94\u82b1\u516b\u95e8\uff0c\u4e5f\u5f88\u590d\u6742\uff0c\u4ec0\u4e48van der Waals\u4f5c\u7528\u3001\u9759\u7535\u4f5c\u7528\u3001\u4f4d\u963b\u4f5c\u7528\u7b49\u7b49\u7406\u8bba\u6a21\u578b\u4e00\u5927\u5806\uff0c\u6240\u4ee5\u591a\u6570\u60c5\u51b5\u4e0b<i>W<\/i>\u7684\u76f4\u63a5\u8868\u8fbe\u5f0f\u90fd\u662f\u627e\u4e2a\u8fd1\u4f3c\u5f0f\u51d1\u5408\u7528\u7684\u3002Prieve and Ruckenstein\uff08J. Colloid Interf. Sci. 1980, 73, 539\uff09\u4e3a\u7403\u5f62\u7c92\u5b50\u5bfc\u51fa\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff1a<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?W=W_{\\infty }+0.25\\left[{\\exp \\left( \\frac{U_{\\textup{max}}}{k_{\\textup{B}}T}\\right ) -1\\right ]}\" title=\"W=W_{\\infty }+0.25\\left[{\\exp \\left( \\frac{U_{\\textup{max}}}{k_{\\textup{B}}T}\\right ) -1\\right ]}\" \/><\/p>\n<p>\u8fd9\u6837\u4e00\u6765\uff0c<i>W<\/i>\u5c31\u8ddfpotential barrier\u6709\u5173\u4e86\u3002<\/p>\n<h3>Smoluchowski\u7684\u8bba\u6587<\/h3>\n<p>\u5f88\u591a\u6587\u7ae0\u4e00\u8bb2\u5230Smoluchowski\u7684\u8bba\u6587\uff0c\u5c31\u4e00\u5b9a\u662f\u5f15\u7528\u4ed6\u57281916\u548c1917\u5e74\u53d1\u8868\u7684\u4e24\u7bc7\u6587\u7ae0\u3002\u6211\u53d1\u73b0\u6709\u5f88\u5927\u4e00\u90e8\u5206\u5f15\u7528\u662f\u9519\u8bef\u7684\uff1a<\/p>\n<blockquote>\n<p>Z. Phys. 1916, 17, 557; <i>ibid.<\/i> 1916, 17, 585; <i>ibid.<\/i> 1917, 92, 129<\/p>\n<\/blockquote>\n<p>\u660e\u773c\u4eba\u4e00\u773c\u5c31\u80fd\u770b\u51fa\u7684\u4e0d\u5bf9\u5c31\u662f\uff1a\u4ec0\u4e48\u671f\u520a1916\u5e74\u624d17\u5377\uff0c\u52301917\u5e74\u5c3192\u5377\u4e86\uff1f\u4f46\u662f\u66f4\u96be\u641e\u6e05\u7684\u5c31\u662f\uff0c1916\u5e7417\u5377\u7684\u90a3\u4e2a\u671f\u520a\u4e5f\u662f\u9519\u7684\u3002<\/p>\n<p>\u5982\u679c\u662f\u7f29\u5199\u4e3a\u201cZ. Phys.\u201d\uff0c\u90a3\u4e48\u5c31\u5e94\u8be5\u662f\u6307Zeitschrift f\u00fcr Physik\uff0c\u73b0\u5728\u7684Eur. Phys. J.\uff0c<a href=\"http:\/\/springerlink.metapress.com\/content\/0939-7922\/\">\u6302\u5728SpringerLink\u4e0a\u9762<\/a>\u3002\u7136\u800c\uff0cSmoluchowski\u57281916\u5e74\u53d1\u8868\u7684\u300117\u5377557\u548c585\u9875\u7684\u4e24\u7bc7\u6587\u7ae0\uff0c\u671f\u520a\u540d\u5e94\u8be5\u662fPhysikalische Zeitschrift\uff0c\u8be5\u520a1945\u5e74\u5c31\u505c\u4e86\u3002\u56e0\u6b64\u6b63\u786e\u7684\u5f15\u7528\u5e94\u8be5\u662fPhys. Z. 1916, 17, 557\u3002\u81f3\u4e8e1917\u5e74\u90a3\u4e2a92\u5377129\u9875\u7684\u8bba\u6587\uff0c\u671f\u520a\u540d\u5176\u5b9e\u662fZeitschrift f\u00fcr Physilalische Chemie\uff0c\u7269\u7406\u8fd8\u5e26\u4e2a\u5316\u5b66\u3002\u8be5\u520a\u73b0\u5728\u8fd8\u6709\uff0c\u653e\u5728\u4e00\u4e2a\u6211\u4e4b\u524d\u6ca1\u542c\u8bf4\u8fc7\u7684\u7f51\u7ad9\u4e0a\uff0c\u800c\u4e14\u53ea\u63d0\u4f9b2000\u5e74\u4ee5\u540e\u7684\u7535\u5b50\u7248\u3002\u56e0\u6b64\u6b63\u786e\u7684\u5f15\u7528\u5e94\u8be5\u662fZ. Phys. Chem. 1917, 92, 129\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u8fd9\u4e09\u7bc7\u8bba\u6587\u73b0\u5728\u90fd\u6ca1\u6709\u5b98\u65b9\u7684\u7535\u5b50\u7248\u4e86\u3002<\/p>\n<p>\u8ba9\u624d\u77e5\u9053\u7684\u6211\u60ca\u8bb6\u7684\u662fSmoluchowski\u5c31\u6b7b\u57281917\u5e74\u3002<\/p>\n<p>\u8c8c\u4f3c\u662f\u6ce2\u5170\u7684\u7f51\u4e0a\u865a\u62df\u56fe\u4e66\u9986<a href=\"http:\/\/matwbn.icm.edu.pl\/spis.php?wyd=4&#038;jez=en\">\u6536\u5f55\u4e86Smoluchowski\u7684\u5f88\u591a\u8bba\u6587<\/a>\uff0c\u5171\u5206\u4e09\u5377\u3002\u5217\u8868\u91cc\u7684\u6807\u9898\u5168\u662f\u539f\u6587\u8bed\u8a00\uff0c\u56e0\u6b64\u6709\u7684\u662f\u5fb7\u8bed\uff0c\u6709\u7684\u662f\u6ce2\u5170\u8bed\u3002\u5c31\u7b97\u7528\u4e86Google Translate\u770b\u8d77\u6765\u4e5f\u5f88\u591f\u545b\u3002\u4f46\u81f3\u5c11\u4f60\u80fd\u53d1\u73b0\uff0cSmoluchowski\u53c2\u4e0e\u4e86\u5f88\u591a\u5e76\u4e0d\u4ee5\u4ed6\u547d\u540d\u7684\u91cd\u8981\u79d1\u5b66\u53d1\u73b0\u3002<\/p>\n<p>\u7ecf\u8fc7\u4e00\u756a\u67e5\u627e\uff0c\u7ec8\u4e8e\u627e\u5230\u5230\u5904\u5f15\u6765\u5f15\u53bb\u7684\u90a3\u4e24\u7bc7\u6587\u7ae0\u7684\u539f\u6587\u4e86\u3002<\/p>\n<p>\u9996\u5148\uff0c\u4e0d\u8981\u4ee5\u4e3a1916\u5e74\u53d1\u8868\u5728Physikalische Zeitschrift\u7684\u662f\u4e24\u7bc7\u6587\u7ae0\u2014\u2014\u90a3\u662f\u4e00\u7bc7\u8bba\u6587\u88ab\u9694\u5f00\u6765\u520a\u767b\u4e86\uff0c\u6807\u9898\u53ea\u6709\u4e00\u4e2a\uff1a Drei Vortr\u00e4ge \u00fcber Diffusion, Brown&#8217;sche Molekularbewegung und Koagulation von Kolloidteilchen\uff0cGoogle Translate\u7ed9\u51fa\u7684\u82f1\u6587\u662fThree lectures on diffusion, Brownian motion and coagulation of colloidal particles\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c1916\u5e74\u53d1\u8868\u5728Phys. Z.\u4e0a\u7684\u90a3\u7bc7\u8bba\u6587\u5fc5\u987b\u540c\u65f6\u628a\u9875\u7801557\u548c587\u6807\u51fa\u6765\u3002\u5982\u679c\u8c01\u81ea\u4f5c\u806a\u660e\u5730\u53ea\u5f15\u7528Phys. Z. 1916, 17, 587\uff0c\u90a3\u5c31\u8d3b\u7b11\u5927\u65b9\u4e86\u3002\u6211\u751a\u81f3\u5efa\u8bae\u628a\u4e24\u6bb5\u9875\u7801\u7528and\u8fde\u8d77\u6765\u5f15\u7528\uff0c\u4ee5\u5f3a\u8c03\u8fd9\u662f<b>\u4e00\u7bc7\u8bba\u6587<\/b>\uff0c\u5373\uff1aSmoluchowski, M., Drei Vortr\u00e4ge \u00fcber Diffusion, Brown&#8217;sche Molekularbewegung und Koagulation von Kolloidteilchen. Phys. Z. 1916, XVII, 557-571 and 587-599\u3002\u539f\u6587<a href=\"http:\/\/matwbn.icm.edu.pl\/ksiazki\/pms\/pms2\/pms2136.pdf\">\u5728\u6b64\u4e0b\u8f7d<\/a>\u3002<\/p>\n<p>\u81f3\u4e8e1917\u5e74\u53d1\u8868\u5728Z. Phys. Chem.\u4e0a\u7684\u8bba\u6587\uff0c\u5b8c\u6574\u7684\u5f15\u7528\u662f\uff1aSmoluchowski, M., Versuch einer mathematischen Theorie der Koagulationskinetik kolloider L\u00f6sungen. Z. Phys. Chem. 1917, XCII (2), 129-168\u3002\u539f\u6587<a href=\"http:\/\/matwbn.icm.edu.pl\/ksiazki\/pms\/pms2\/pms2137.pdf\">\u5728\u6b64\u4e0b\u8f7d<\/a>\u3002<\/p>\n<p>\u4ee5\u4e0a\u662f\u6211\u76f8\u4fe1\u6700\u51c6\u786e\u7684\u8bba\u6587\u4fe1\u606f\u4e86\uff0c\u539f\u6587\u4e5f\u662f\u5f88\u96be\u5f97\u7684\u2014\u2014\u867d\u7136\u770b\u4e0d\u61c2\u3002<\/p>\n<p>\u9664\u4e86\u5927\u5bb6\u5e38\u5f15\u7684\u4e0a\u9762\u4e24\u7bc7\u8bba\u6587\u4e4b\u5916\uff0c\u5173\u4e8ecoagulation\u7684\u8bba\u6587\u8fd8\u6709\u4e00\u7bc7\u80fd\u591f\u5728\u51fa\u7248\u5546\u7f51\u7ad9\u4e0a\u4e0b\u8f7d\u5230\u7535\u5b50\u7248\u7684\uff0c\u90a3\u5c31\u662f<a href=\"http:\/\/dx.doi.org\/10.1007\/BF01427232\">Kolloid-Z. 1917, XXI, 98-104<\/a>\u3002\u7f51\u7ad9\u4e0a\u663e\u793a\u8fd9\u7bc7\u8bba\u6587\u53ea\u88ab3\u6b21\u5f15\u7528\uff0c\u5206\u522b\u662f1956\u5e74\uff0c2010\u5e74\u548c2011\u5e74\u3002\u6709\u8da3\u30022011\u5e74\u90a3\u7bc7\u8fd8\u662f\u4e2aJ. Chem. Phys.\u5462\u3002<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 2406 -->","protected":false},"excerpt":{"rendered":"<p>\u5723\u6bcd\u739b\u4e3d\u4e9a\u7684Smoluchowski \u6700\u8fd1\u5728\u5b66\u4e60Smoluchowski\u7684coagulation\u7406\u8bba\u3002\u4e0aGoogle\u641c\u7d22\u201cSmoluchowski\u7406\u8bba\u201d\uff0c\u7b2c\u4e00\u4e2a\u641c\u7d22\u7ed3\u679c\u7684\u6807\u9898\u4e3a\u201c\u5723\u6bcd\u739b\u4e3d\u4e9a\u7684Smoluchowski\u201d\u3002\u539f\u6765\u662f\u81ea\u52a8\u7ffb\u8bd1\u8f6f\u4ef6\u5f04\u7684\uff0c\u628aSmoluchowski\u7684first name\u7ed9\u8bd1\u8fc7\u6765\u4e86\u3002\u6309\u7406\u4e5f\u6ca1\u9519\u3002\u8bf4\u4e0d\u5b9aSmoluchowski\u7684\u7236\u6bcd\u7ed9\u8fd9\u5b69\u5b50\u9009\u62e9\u8fd9\u4e2a\u540d\u5b57\u5c31\u662f\u5e0c\u671b\u5b83\u80fd\u50cf\u5723\u6bcd\u7684\u5b69\u5b50\u90a3\u6837blessed\u3002 \u5173\u4e8e\u5982\u4f55\u901a\u8fc7\u52a8\u6001\u5149\u6563\u5c04\u6d4bpotential barrier \u6211\u4e4b\u6240\u4ee5\u8981\u770bSmoluchowski\u7406\u8bba\uff0c\u662f\u7531\u4e8e\u9047\u5230\u4e86\u4e00\u4e9b\u6587\u7ae0\u901a\u8fc7\u52a8\u6001\u5149\u6563\u5c04\uff08DLS\uff09\u6765\u83b7\u5f97\u7c92\u5b50\u95f4\u7684pair potential\u7684\u90a3\u4e2a\u6240\u8c13primary maximum\uff0c\u6216\u8005\u8bf4potential barrier\uff08Umax\uff09\u3002DLS\u53ef\u4ee5\u7528\u6765\u6d4b\u5e73\u5747\u6269\u6563\u7cfb\u6570\u3002\u5982\u679c\u6837\u54c1\u968f\u65f6\u95f4\u4e0d\u65ad\u53d1\u751faggrigation\uff0c\u90a3\u4e48\u5e73\u5747\u6269\u6563\u7cfb\u6570\u5c31\u4f1a\u968f\u65f6\u95f4\u53d8\u5316\uff0c\u6d4b\u51fa\u3002Pusey\u7b49\uff08J. Chem. Phys. 1982, 77, 4270\uff09\u7ed9\u51fa\u4e86\u7ed9\u5b9a\u5c3a\u5bf8\u5206\u5e03\u7684\u7c92\u5b50\u4f53\u7cfb\u7684\u5e73\u5747\u6269\u6563\u7cfb\u6570\u8868\u8fbe\u5f0f\uff1a \u5176\u4e2d\u4e0b\u6807p\u662f\u6307\u7b2cp\u79cd\u5c3a\u5bf8\u3002N\u662f\u4e2a\u6570\uff0cf\u662f\u6563\u5c04\u5f3a\u5ea6\u3002\u5bf9\u4e8e\u5c3a\u5bf8\u5206\u5e03\u672c\u6765\u662f\u5355\u5206\u6563\u7684\u7c92\u5b50\uff0c\u5728\u805a\u96c6\u8fc7\u7a0b\u4e2d\u5c31\u4f1a\u6709\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u5230p\u805a\u4f53\u7b49\u5927\u5c0f\u4e0d\u4e00\u7684\u5355\u5143\u5b58\u5728\uff0c\u56e0\u6b64\u662f\u4e00\u4e2a\u591a\u5206\u6563\u4f53\u7cfb\uff0c\u9002\u7528Pusey\u7684\u5f0f\u5b50\u3002\u800c\u4e14\u5404p\u805a\u4f53\u7684\u6570\u91cf\u90fd\u968f\u65f6\u95f4\u53d8\u5316\uff0c\u5373\u6574\u4e2a\u5c3a\u5bf8\u5206\u5e03\u5728\u968f\u65f6\u95f4\u53d8\u5316\u3002\u56e0\u6b64Pusey\u7684\u90a3\u6761\u5f0f\u5b50\u5c31\u8981\u52a0\u4e0a\u65f6\u95f4\u4f9d\u8d56\u6027\uff0c\u53d8\u6210\u4e86\uff1a Versmold &amp; H&auml;rtl\uff08J. Chem. Phys. 1983, 79, 4006\uff09\u901a\u8fc7\u7b80\u5355\u5047\u8bbe\u5404p\u805a\u4f53\u90fd\u662f\u7403\u4f53\uff0c\u4ee5\u4fbf\u90a3\u4e2a\u6269\u6563\u7cfb\u6570\u4e0e\u5c3a\u5bf8\u7684\u5173\u7cfb\u5f0f\u80fd\u5e94\u7528\u5728\u5404\u4e2ap\u805a\u4f53\u4e0a\uff1b\u53e6\u6839\u636e\u5149\u6563\u5c04\u539f\u7406\uff0c\u6563\u5c04\u5f3a\u5ea6f\u8ddf\u7c92\u5b50\u4f53\u79ef\uff08\u534a\u5f84\u7684\u7acb\u65b9\uff09\u6709\u5173\u3002\u8fd9\u6837\u5c31\u628aPusey\u7684\u5f0f\u5b50\u4e2dfp\u548cD0,p\u76f4\u63a5\u7528ap\u4ee3\u66ff\u4e86\uff0c\u53d8\u6210\uff1a Smoluchowski\u65b9\u7a0bNp(t\/t1\/2)=&#8230;\u7684\u7528\u5904\u5c31\u662f\u7528\u6765\u7b97\u4e0a\u5f0f\u90a3\u4e24\u4e2ap\u7684\u77e9\u3002\u636eVersmold &amp; H&auml;rtl\u7684\u6587\u7ae0\u6240\u5f15\u8ff0\uff0cp\u7684\u5747\u65b9\u503c\uff086\/3\uff09\u4e4b\u524d\u6709\u4eba\u7ed9\u51fa\u89e3\u6790\u89e3\u4e86\u3002\u53ef\u8fd95\/3\u9636\u77e9\u53ef\u600e\u4e48\u529e\u5462\uff1fVersmold &amp; H&auml;rtl\u53ea\u80fd\u5728\u65f6\u95f4t\/t1\/2\u5f88\u5c0f\u7684\u6761\u4ef6\u4e0b\uff08\u5373aggregation\u521a\u53d1\u751f\u6ca1\u591a\u4e45\uff09\u628aSmoluchowski\u65b9\u7a0b\u7ed9\u5c55\u5f00\u4e86\u53d6\u8fd1\u4f3c\uff0c\u8fd9\u6837\u7684\u8bddp\u7684n\/3\u9636\u77e9\u968ft\/t1\/2\u7684\u53d8\u5316\u5c31\u90fd\u80fd\u8ba1\u7b97\u3002\u4e0d\u8fc7\u8fd9\u6837\u7ed9\u51fa\u7684\u8868\u8fbe\u5f0f\u662f\u4e2a\u7ebf\u6027\u5f0f\uff0c\u53ea\u9002\u7528\u4e8e\u805a\u96c6\u53cd\u5e94\u7684\u521d\u671f\u3002\u81f3\u4e8e\u9002\u7528\u4e8e\u6574\u4e2a\u65f6\u95f4\u57df\u7684\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u7528\u8ba1\u7b97\u673a\u7ed9\u51fa\u6570\u503c\u89e3\u3002 \u4ee5\u4e0a\u7684\u5de5\u4f5c\uff0c\u901a\u8fc7Smoluchowski\u65b9\u7a0b\uff0c\u7ed9\u51fa\u4e86\u7c92\u5b50\u4f53\u7cfb\u5728\u805a\u96c6\u8fc7\u7a0b\u4e2d\u6269\u6563\u7cfb\u6570\u7684\u65f6\u95f4\u4f9d\u901f\u5173\u7cfbD(t)\u7684\u8868\u8fbe\u5f0f\uff0c\u5f0f\u4e2d\u552f\u4e00\u7684\u53c2\u6570\u662f\u90a3\u4e2at1\/2\uff0c\u6240\u4ee5\uff0c\u62ff\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u53bb\u62df\u5408\u5b9e\u6d4b\u6570\u636e\uff0c\u5c31\u80fd\u5f97\u5230\u8fd9\u4e2at1\/2\u4e86\u3002\u8fd9\u4e2at1\/2\u8ddf\u805a\u96c6\u53cd\u5e94\u7684\u901f\u7387\u5e38\u6570k\u76f4\u63a5\u6709\u5173\uff1ak=1\/(t1\/2N0)\uff0c\u5176\u4e2dN0\u662f\u6700\u521d\u7684\u7c92\u5b50\u5bc6\u5ea6\uff08\u4e2a\u6570\u6bd4\u4f53\u79ef\uff09\u3002 \u6240\u4ee5\uff0c\u7528\u52a8\u6001\u5149\u6563\u5c04\u53ef\u4ee5\u6d4b\u51fak\u3002 k\u53c8\u8ddf\u7c92\u5b50\u95f4\u7684pair potential\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u9996\u5148\uff0c\u8fd9\u4e2a\u901f\u7387\u5e38\u6570\u662f\u805a\u96c6\u53cd\u5e94\u7684\u6570\u7387\u5e38\u6570\uff0c\u4e24\u4e2a\u7c92\u5b50\u78b0\u649e\u540e\u8981\u53d1\u751f\u805a\u96c6\uff0c\u5b83\u4eec\u5f53\u7136\u8981\u514b\u670d\u6389\u4e24\u8005\u95f4\u7684potential barrier\u3002\u56e0\u6b64\u7c92\u5b50\u95f4\u7684potential barrier\u5c31\u51b3\u5b9a\u4e86\u6709\u6548\u78b0\u649e\u5360\u603b\u78b0\u649e\u6570\u4e4b\u6bd4\u4f8b\u3002\u603b\u78b0\u649e\u6570\u65e0\u975e\u5c31\u662f\u5e03\u6717\u8fd0\u52a8\u51b3\u5b9a\uff08\u7c98\u5ea6\u3001\u5c3a\u5bf8\u90fd\u5b9a\u4e86\u8fd9\u4e2a\u5c31\u662f\u5b9a\u7684\uff09\u3002\u56e0\u6b64\uff0c\u90a3\u4e2a\u6bd4\u4f8b\u2014\u2014\u79f0\u4e3astability ratio\uff0cW\u2014\u2014\u5c31\u8ddfpotential barrier\u76f4\u63a5\u6709\u5173\u4e86\uff1a \u636e\u4f20\u4e0a\u5f0f\u662fN. Fuch\u7ed9\u7684\uff0c\u4e4b\u6240\u4ee5\u8bf4\u201c\u636e\u4f20\u201d\uff0c\u662f\u56e0\u4e3a\u6211\u81ea\u5df1\u6ca1\u6709\u770b\u8fc7N. Fuch\u7684\u8bba\u6587\uff08\uff09\u2014\u2014\u5fb7\u8bed\u7684\uff0c\u770b\u4e0d\u61c2\u3002\u6211\u53ea\u77e5\u9053\u5f88\u591a\u4eba\u4e00\u63d0\u5230stability ratio\uff0c\u5c31\u5f15N. Fuch\u8fd9\u7bc7\u4e1c\u897f\u3002 \u79ef\u5206\u5f0f\u4e2d\u7684U(r)\u5f62\u5f0f\u4e94\u82b1\u516b\u95e8\uff0c\u4e5f\u5f88\u590d\u6742\uff0c\u4ec0\u4e48van der Waals\u4f5c\u7528\u3001\u9759\u7535\u4f5c\u7528\u3001\u4f4d\u963b\u4f5c\u7528\u7b49\u7b49\u7406\u8bba\u6a21\u578b\u4e00\u5927\u5806\uff0c\u6240\u4ee5\u591a\u6570\u60c5\u51b5\u4e0bW\u7684\u76f4\u63a5\u8868\u8fbe\u5f0f\u90fd\u662f\u627e\u4e2a\u8fd1\u4f3c\u5f0f\u51d1\u5408\u7528\u7684\u3002Prieve and Ruckenstein\uff08J. Colloid Interf. Sci. 1980, 73, 539\uff09\u4e3a\u7403\u5f62\u7c92\u5b50\u5bfc\u51fa\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff1a \u8fd9\u6837\u4e00\u6765\uff0cW\u5c31\u8ddfpotential barrier\u6709\u5173\u4e86\u3002 Smoluchowski\u7684\u8bba\u6587 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[237],"tags":[34],"class_list":["post-2406","post","type-post","status-publish","format-standard","hentry","category-featured","tag-colloid"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1aPvF-CO","jetpack-related-posts":[{"id":9291,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9291","url_meta":{"origin":2406,"position":0},"title":"\u201c\u5fae\u6d41\u53d8\u201d\u672f\u8bed\u53f2","author":"Andrew","date":"2025\u5e7410\u670819\u65e5","format":false,"excerpt":"\u201c\u5fae\u6d41\u53d8\u201d\uff08microrheology\uff09\u5728\u6700\u8fd1\u51e0\u5e74\u7684\u6587\u732e\u4e2d\u662f\u4e13\u6307III. \u901a\u8fc7\u80f6\u4f53\u7c92\u5b50\u7684\u70ed\u8fd0\u52a8\u7edf\u8ba1\u89c4\u5f8b\u53cd\u63a8\u60ac\u6d6e\u4ecb\u8d28\u7684\u6d41\u53d8\u6027\u8d28\u7684\u4e00\u79cd\u5b9e\u9a8c\u7814\u7a76\u3002\u8fd9\u4e5f\u662f\u6211\u73b0\u5728\u7814\u7a76\u65b9\u5411\u4e4b\u4e00\u3002\u4f46\u662f\uff0c\u8fd9\u4e2a\u672f\u8bed\u6700\u65e9\u7684\u610f\u4e49\u8ddf\u73b0\u5728\u6709\u4e9b\u533a\u522b\u3002 \u6839\u636e\u6211\u67e5\u5230\u7684\u7ed3\u679c\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u6700\u65e9\u51fa\u73b0\u5728M. Reiner\u7684\u6d41\u53d8\u5b66\u8bb2\u4e49\uff08Markus Reiner (1943), Ten Lectures on Theoretical Rheology, Rubin Mass\uff09\u4e2d\u7684\u7b2c\u4e03\u8bb2\u3002\u8fd9\u4e2a\u5957\u8bb2\u4e49\u540e\u6765\u5206\u522b\u57281949\u5e74\u548c1960\u5e74\u51fa\u4e86\u7b2c\u4e8c\u548c\u7b2c\u4e09\u7248\u3002\u7b2c\u4e09\u7248\u6709\u4e2d\u8bd1\u672c\uff1aM. \u96f7\u8bb7\u8457\uff0c\u90ed\u6709\u4e2d\u7b49\u8bd1\u300a\u7406\u8bba\u6d41\u53d8\u5b66\u8bb2\u4e49\u300b\uff0c\u7531\u79d1\u5b66\u51fa\u7248\u793e\u4e8e1965\u51fa\u7248\u3002\u5728\u5f53\u65f6\u8fd9\u4e2a\u8bcd\u5927\u6982\u662f\u6307I. \u4ece\u5fae\u89c2\u7ed3\u6784\u63a8\u51fa\u5b8f\u89c2\u7cfb\u7edf\u6d41\u53d8\u5b66\u6027\u8d28\u7684\u7406\u8bba\u7814\u7a76\uff0c\u4f3c\u4e4e\u662f\u7528\u4e8e\u4e0e\u57fa\u4e8e\u8fde\u7eed\u4ecb\u8d28\u5047\u5b9a\u7684\u7406\u8bba\u76f8\u533a\u522b\u3002\u540e\u8005\u88ab\u79f0\u4f5c\u201cmacrorheology\u201d\u3002 \u5927\u6982\u76f8\u540c\u7684\u65f6\u671f\uff0c\u80f6\u4f53\u7c92\u5b50\u60ac\u6d6e\u6db2\u6d41\u53d8\u5b66\u7684\u5148\u9a71Stanley G. Mason\uff081914-1987\uff09\u5927\u91cf\u4f7f\u7528\u8fd9\u4e2a\u8bcd\u6765\u63cf\u8ff0\u4ed6\u7814\u7a76\u7684\u95ee\u9898\u3002\u5173\u4e8eMason\u7ecf\u5386\u7684\u4e00\u4e9b\u8d44\u6599\u53ef\u89c1\u4ed6\u7684\u81ea\u8ff0\u548c\u540e\u8f88\u5199\u7684appreciation\u3002Mason\u57281950\u5e74\u4ee3\u5c31\u5f00\u59cb\u6b63\u5f0f\u7814\u7a76\u60ac\u6d6e\u7c92\u5b50\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u3002\u4ed6\u521b\u7acb\u7684\u7814\u7a76\u65b9\u6cd5\u662fII. \u901a\u8fc7\u5b9e\u9a8c\u89c2\u5bdf\u7c92\u5b50\u5468\u56f4\u7684\u6d41\u573a\u6765\u9a8c\u8bc1\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u3002\u56e0\u6b64\uff0c\u5230\u4e86Mason\u8fd9\u91cc\uff0c\u201cmicrorheology\u201d\u7684\u610f\u4e49\u5c31\u4ece\u7406\u8bba\u6a21\u578b\u53d8\u4e3a\u5b9e\u9a8c\u624b\u6bb5\u3002Mason\u4e5f\u63a8\u5bfc\u8fc7\u80f6\u4f53\u6d41\u53d8\u5b66\u7406\u8bba\uff0c\u4f46\u4ed6\u548c\u4ed6\u7684\u5b66\u751f\u4e0d\u7528\u201cmicrorheology\u201d\u4e00\u8bcd\u63cf\u8481\u8fd9\u4e9b\u7406\u8bba\u5de5\u4f5c\u3002 Mason\u7684\u53ca\u5176\u5b66\u751f\u7684\u540e\u7eed\u5de5\u4f5c\u4e00\u76f4\u6301\u7eed\u52301970\u5e74\u4ee3\u3002\u5728\u8fd9\u6bb5\u65f6\u95f4\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u51e0\u4e4e\u53ea\u51fa\u73b0\u5728\u4ed6\u4eec\u53d1\u8868\u7684\u5de5\u4f5c\u5f53\u4e2d\u3002\u4e5f\u6709\u96f6\u661f\u613f\u610f\u4f7f\u7528Reiner\u8bb2\u4e49\u7684\u8001\u610f\u4e49\u7684\u8bba\u6587\uff0c\u5305\u62ec\u51af\u5143\u6862\u5148\u751f\u30021970\u5e74\u4ee3\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u88ab\u8840\u6db2\u6d41\u53d8\u5b66\u9886\u57df\u5927\u91cf\u91c7\u7528\uff0c\u8fd9\u4e5f\u4ecd\u662f\u5f52\u56e0\u4e8eMason\u7684\u5de5\u4f5c\u5bf9\u8fd9\u4e00\u9886\u57df\u7684\u5f71\u54cd\u529b\u3002 \u6211\u80fd\u627e\u5230\u7684\u7b2c\u4e00\u4e2a\u610f\u4e49\u53d8\u6210\u73b0\u5728\u7684\u7b2cIII\u79cd\u7684\u6700\u65e9\u8bba\u6587\u662f1985\u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u3002 \u4e0e\u201cmicrorheology\u201d\u4e00\u8bcd\u5341\u5206\u76f8\u5173\u7684\u8fd8\u6709\u201cmicroviscosity\u201d\u3002\u8fd9\u4e2a\u8bcd\u53cd\u800c\u6700\u65e9\u5c31\u8fbe\u5230\u4e86\u4eca\u5929\u5bf9microrheology\u5e94\u8be5\u8fbe\u5230\u7684\u7406\u89e3\u3002\u57281929\u5e74\u7684\u7b2c\u4e00\u5c4a\u7f8e\u56fd\u6d41\u53d8\u5b66\u5e74\u4f1a\u4e0a\uff0cE. Kraemer & R. Williamson\u533a\u5206\u4e86\u51e0\u4e2a\u5c42\u6b21\u7684\u201c\u6469\u64e6\u201d\uff08friction\uff09\u3002\u4e00\u662f\u5b8f\u89c2\u4f53\u7cfb\u7684\u7c98\u5ea6\uff0c\u4e8c\u662f\u7c92\u5b50\u4e0e\u5468\u56f4\u6d41\u573a\u754c\u9762\u5904\u7684\u6469\u64e6\uff0c\u4e09\u662f\u7c92\u5b50\u5f62\u53d8\u7684\u5185\u90e8\u6469\u64e6\u3002\u201cmicroviscosity\u201d\u6307\u7684\u5c31\u662f\u5728IV. \u5fae\u89c2\u5c3a\u5ea6\u4e0b\u7684\u7c98\u5ea6\u2014\u2014\u5b83\u5e38\u5e38\u4e0e\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u5bf9\u540c\u4e00\u7cfb\u7edf\u6d4b\u5f97\u7684\u7c98\u5ea6\u660e\u663e\u4e0d\u540c\u3002\u8fd9\u4ef6\u4e8b\u65e9\u5728\u201c\u80f6\u4f53\u201d\uff08colloid\uff09\u4e00\u8bcd\u7684\u675c\u64b0\u8005Thomas Graham\u57281861\u5e74\u7684\u7814\u7a76\u4e2d\u5c31\u53d1\u73b0\u4e86\u3002\u76d0\u5728\u660e\u80f6\u6216\u743c\u8102\u51dd\u80f6\u4e2d\u7684\u6269\u6563\u6bd4\u5c11\u6162\u4e0d\u4e86\u591a\u5c11\uff0c\u4f46\u524d\u8005\u7684\u7c98\u5ea6\u6bd4\u6c34\u9ad8\u597d\u51e0\u4e2a\u6570\u91cf\u7ea7\u3002\u56e0\u6b64\u8fd9\u4ee4\u4eba\u76f8\u4fe1\uff0c\u5fae\u89c2\u5c3a\u5ea6\u7269\u4f53\u611f\u53d7\u5230\u7684\u6db2\u4f53\u7684\u7c98\u5ea6\u662f\u8ddf\u5b8f\u89c2\u6d4b\u91cf\u503c\u4e0d\u540c\u7684\u3002\u5177\u4f53\u5728\u8fd9\u4e00\u5b9e\u9a8c\u73b0\u8c61\u4e2d\uff0c\u7814\u7a76\u8005\u751a\u81f3\u662f\u901a\u8fc7\u6269\u6563\u7684\u6548\u679c\u6765\u7406\u89e3\u7c98\u5ea6\u3002\u8fd9\u662f\u5728Einstein--Stokes\u5173\u7cfb\u7684\u7406\u8bba\u57fa\u7840\u4e0a\u7684\u8ba4\u8bc6\u89d2\u5ea6\uff0c\u628a\u5b9e\u9a8c\u7ed3\u679c\u5173\u4e8eEinstein--Stokes\u5173\u7cfb\u7684\u504f\u79bb\u5f53\u4f5c\u7c98\u5ea6\u4e0d\u540c\u3002\u4eca\u5929\u6211\u4eec\u8fd8\u6709\u53e6\u4e00\u79cd\u505a\u6cd5\uff0c\u90a3\u5c31\u662f\u628a\u5b9e\u9a8c\u7ed3\u679c\u5173\u4e8eEinstein--Stokes\u5173\u7cfb\u7684\u504f\u79bb\u5f53\u4f5c\u534a\u5f84\u4e0d\u540c\uff0c\u5b9a\u4e49\u51fa\u201c\u6d41\u4f53\u52a8\u529b\u5b66\u534a\u5f84\u201d\u3002\u8fd9\u4e24\u54b1\u505a\u6cd5\u7684\u4eba\u4e4b\u95f4\u5f88\u5c11\u770b\u5230\u6709\u4ea4\u53c9\u7684\uff0c\u66f4\u522b\u8bf4\u6709\u4eba\u53bbreconcile\u8fd9\u4e24\u8005\u3002\u8fd9\u53ef\u80fd\u662f\u7531\u4e8e\u5b9e\u9a8c\u65b9\u6cd5\u4e0d\u540c\u3002\u4e00\u6d3e\u4eba\u6d4b\u91cf\u5b8f\u89c2\u7cfb\u7edf\u7684\u7c98\u5ea6\uff0c\u548c\u5206\u5b50\u7684\u6269\u6563\u7cfb\u6570\u3002\u7531\u4e8e\u5206\u5b50\u7ed3\u6784\u662f\u660e\u786e\u7684\uff0c\u8fd9\u6d3e\u4eba\u662f\u4e0d\u4f1a\u6000\u7591\u5206\u5b50\u8fd8\u6709\u53e6\u4e00\u79cd\u201c\u534a\u5f84\u201d\u3002\u53e6\u4e00\u6d3e\u4eba\u7528\u52a8\u6001\u5149\u6563\u5c04\u6d4b\u80f6\u4f53\u7c92\u5b50\u5728\u60ac\u6d6e\u6db2\u4e2d\u6216\u805a\u5408\u7269\u5728\u6eb6\u6db2\u4e2d\u7684\u534a\u5f84\uff0c\u5e76\u4e0e\u7535\u5b50\u663e\u5fae\u955c\u6216\u89d2\u5ea6\u4f9d\u8d56\u6563\u5c04\u7684\u7ed3\u679c\uff08\u5747\u65b9\u56de\u8f6c\u534a\u5f84\uff09\u76f8\u6bd4\u8f83\u3002\u7279\u522b\u662f\u5bf9\u4e8e\u805a\u5408\u7269\u8bd5\u6837\uff0c\u7531\u4e8e\u5176\u5206\u5b50\u5c3a\u5bf8\u53ea\u6709\u5e73\u5747\u6982\u5ff5\uff0c\u5728\u6eb6\u6db2\u4e2d\u7684\u5e73\u5747\u5c3a\u5bf8\u8fd8\u53d7\u6eb6\u5242\u6eb6\u8d28\u76f8\u4e92\u4f5c\u7528\u4ee5\u53ca\u6d41\u4f53\u52a8\u529b\u5b66\u76f8\u4e92\u4f5c\u7528\u7684\u5f71\u54cd\u3002\u800c\u6269\u6563\u7cfb\u6570\u88ab\u9690\u542b\u5728\u52a8\u6001\u5149\u6563\u5c04\u7684\u57fa\u672c\u539f\u7406\u5f53\u4e2d\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":4846,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4846","url_meta":{"origin":2406,"position":1},"title":"\u51dd\u80f6\u5316\u8fc7\u7a0b\u7684\u677e\u5f1b\u65f6\u95f4","author":"Andrew","date":"2012\u5e748\u67089\u65e5","format":false,"excerpt":"\u524d\u6bb5\u65f6\u95f4\uff0c\u6211\u82b1\u65f6\u95f4\u641e\u6e05\u695a\u4e86\u65f6\u6e29\u53e0\u52a0\uff08\u4ee5\u53ca\u6240\u6709\u5173\u4e8e\u76f8\u5173\u51fd\u6570\u548c\u54cd\u5e94\u51fd\u6570\u7684\u53e0\u52a0\uff09\u5f97\u5230\u7684\u677e\u5f1b\u65f6\u95f4\u6bd4\u503c\uff0c\u662f\u4ec0\u4e48\u677e\u5f1b\u65f6\u95f4\u3002\u5728KWW\u5f62\u5f0f\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u53ef\u8bc1\u5b9e\u53e0\u52a0\u56e0\u5b50\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4\u4e4b\u6bd4\u3002\u6700\u8fd1\u8fd9\u51e0\u5929\uff0c\u6211\u4e3b\u8981\u60f3\u641e\u6e05\u695a\uff0c\u51dd\u80f6\u5316\u8fc7\u7a0b\u4e2d\u7684\u677e\u5f1b\u65f6\u95f4\u662f\u4ec0\u4e48\u677e\u5f1b\u65f6\u95f4\u3002\u8fd9\u91cc\u7684\u51dd\u80f6\u5316\u662f\u6307\u4e0d\u53ef\u9006\u805a\u96c6\uff08irreversible aggregation\uff09\u8fc7\u7a0b\u4e2d\u53d1\u751f\u6e1d\u6e17\u7684\u51dd\u80f6\u5316\u3002 \u805a\u96c6\u5bfc\u81f4\u7684\u51dd\u80f6\u5316\uff0c\u662f\u7c92\u5b50\u53d1\u751f\u4e0d\u53ef\u9006\u805a\u96c6\uff08DLCA\u6216RLCA\u673a\u7406\uff09\u5f62\u6210cluster\uff0c\u7136\u540ecluster\u4e4b\u95f4\u805a\u96c6\u6700\u540e\u5f62\u6210\u65e0\u9650\u7f51\u7edc\uff08\u6216\u8d2f\u7a7f\u6837\u54c1\u7684\u7f51\u7edc\uff09\u7684\u8fc7\u7a0b\u3002\u5f62\u6210\u7684cluster\u548c\u7f51\u7edc\u90fd\u662f\u5206\u5f62\u3002\u7531cluster\u8fde\u63a5\u5f62\u6210\u7684\u7f51\u7edc\u8fd8\u6709\u5f88\u591a\u6d1e\uff0c\u53ef\u501f\u7528\u73bb\u7483\u7684cage\u6982\u5ff5\u3002\u5269\u4f59\u7684\u81ea\u7531cluster\u5c31\u88ab\u9650\u5236\u5728cage\u91cc\uff0c\u5b83\u4e0e\u5176\u8bf4\u8981\u9003\u79bbcage\u6269\u6563\u5230\u5916\u9762\u53bb\uff0c\u4e0d\u5982\u8bf4\u76f4\u63a5\u5c31\u52a0\u5165\u5230\u5df2\u6709\u7f51\u7edc\u91cc\u53bb\u4e86\u3002 \u5728\u51dd\u80f6\u5316\u70b9\uff08\u6e1d\u6e17\u70b9\uff09\u4e4b\u524d\u662f\u53ef\u4ee5\u7531Smoluchowski\u65b9\u7a0b\u6765\u63cf\u8ff0\u7684\u3002\u5047\u5982\u505a\u52a8\u6001\u5149\u6563\u5c04\uff0c\u6240\u8c13\u677e\u5f1b\u65f6\u95f4\u662f\u7528\u4e0b\u5f0f\u53bb\u62df\u5408\u52a8\u6001\u7ed3\u6784\u56e0\u5b50\u5f97\u5230\u7684\uff1a \u5176\u4e2d\u6240\u4ee5\u03c4\u6b63\u6bd4\u4e8eRh\u3002\u540e\u8005\u968f\u65f6\u95f4\u7684\u589e\u957f\u5c31\u662f\u524d\u8005\u968f\u65f6\u95f4\u7684\u589e\u957f\u3002\u51dd\u80f6\u5316\u524d\u671f\u7684\u805a\u96c6\u7406\u8bba\uff08Smoluchowski\u65b9\u7a0b\uff09\u5c31\u8fd9\u4e48\u8ddfdynamics\u8054\u7cfb\u8d77\u6765\u4e86 \u95ee\u9898\u5728\u4e8e\uff0c\u51dd\u80f6\u5316\u70b9\u4e4b\u540e\u600e\u4e48\u529e\u3002\u901a\u8fc7\u53e0\u52a0\u5f97\u5230\u7684\u56e0\u5b50\uff0c\u5e94\u8be5\u4ecd\u662f\u4e00\u4e2a\u5177\u6709\u677e\u5f1b\u65f6\u95f4\u6982\u5ff5\u7684\u91cf\u3002\u4f46\u662f\u51dd\u80f6\u5316\u4e4b\u540e\u4f53\u7cfb\u7684\u677e\u5f1b\u65f6\u95f4\u53d1\u6563\u4e86\u3002\u53e0\u52a0\u5f97\u5230\u4e00\u4e2a\u03c4\uff0c\u53c8\u4ee3\u8868\u4ec0\u4e48\u5462\uff1f\u6211\u89c9\u5f97\u8fd9\u662f\u5269\u4f59\u81ea\u7531cluster\u4ececage\u4e2d\u9003\u79bb\u7684\u5e73\u5747\u65f6\u95f4\u3002\u505a\u52a8\u6001\u5149\u6563\u5c04\u7684\u65f6\u5019\uff0c\u51dd\u80f6\u5316\u4e4b\u540e\u7684\u52a8\u6001\u7ed3\u6784\u56e0\u5b50\u4e0d\u80fd\u5b8c\u5168\u8870\u51cf\uff0c\u800c\u662f\u8fbe\u5230\u4e00\u4e2a\u6709\u9650\u5e73\u53f0\u503c\uff0c\u8be5\u503c\u662fDebye-Waller factor\uff0c\u53c8\u79f0\u4e3aEdwards-Anderson order parameter\u3002Krall\u7b49\u4e3a\u4e86\u4ece\u8fd9\u79cd\u5f62\u72b6\u7684\u52a8\u6001\u7ed3\u6784\u56e0\u5b50\u63d0\u53d6\u51fa\u4e00\u4e9b\u7ed3\u6784\u4fe1\u606f\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u6a21\u578b\uff0c\u5177\u4f53\u4e0d\u8be6\u8ff0\u4e86\uff0c\u5176\u52a8\u6001\u7ed3\u6784\u56e0\u5b50\u7684\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a \u6240\u4ee5\uff0c\u5047\u5982\u51dd\u80f6\u5316\u4e4b\u540e\u76f8\u5173\u51fd\u6570\u6216\u76f8\u5e94\u51fd\u6570\u4ecd\u6709\u4ec0\u4e48\u53e0\u52a0\u6027\uff0c\u53e0\u52a0\u56e0\u5b50\u5c31\u662f\u4e0a\u5f0f\u8fd9\u4e2a\u03c4\u7684\u6bd4\u503c\uff0c\u800c\u8fd9\u4e2a\u03c4\u8ddfblob\u7684\u5c3a\u5bf8R\u548c\u5f39\u6027\u7cfb\u6570k\u6709\u5173\u3002\u4e8b\u5b9e\u4e0a\uff0c\u4e0a\u5f0f\u7b26\u5408 \u56e0\u6b64<\u0394r^2>\u5c31\u662fcage\u7684\u5747\u65b9\u534a\u5f84\u3002\u03c4\u8ddf<\u0394r^2>\u6210\u53cd\u6bd4\uff0c\u6240\u4ee5\u51dd\u80f6\u5316\u70b9\u540e\u03c4\u7684\u7ee7\u7eed\u589e\u957f\uff0c\u53cd\u6620\u7684\u4e0d\u662f\u4f53\u7cfb\u8fd8\u80fd\u677e\u5f1b\uff0c\u800c\u662fcage\u4e0d\u65ad\u7f29\u5c0f\uff0c\u8fd9\u662f\u5269\u4f59\u81ea\u7531cluster\u4e0d\u65ad\u52a0\u5165\u5230\u4e3b\u7f51\u7edc\u7684\u7ed3\u679c\u3002 \u6700\u540e\u91cd\u65b0\u5f3a\u8c03\u4e00\u6b21\u6982\u5ff5\u6027\u7684\u95ee\u9898\uff0c\u7531\u4e8e\u662f\u201c\u4e0d\u53ef\u9006\u805a\u96c6\u201d\u5f62\u6210\u7684\u51dd\u80f6\uff08\u5316\u5b66\u51dd\u80f6\uff09\uff0c\u6240\u4ee5\u51dd\u80f6\u5316\u4e4b\u540e\u5c31\u52a8\u4e0d\u4e86\u4e86\uff0c\u4e0d\u5b58\u5728\u6709\u9650\u677e\u5f1b\u65f6\u95f4\uff0c\u8fd9\u8ddf\u5b9e\u9645\u7684\u7269\u7406\u51dd\u80f6\u4e0d\u540c\u3002\u6211\u4eec\u90fd\u77e5\u9053\uff0c\u5b9e\u9645\u4e0a\u7684\u80f6\u4f53\u51dd\u80f6\u90fd\u662f\u7269\u7406\u51dd\u80f6\uff0c\u51dd\u80f6\u5316\u70b9\u540e\u53ef\u4ee5\u8c08\u8bba\u201c\u4e00\u4e2a\u5f88\u5927\u7684\u677e\u5f1b\u65f6\u95f4\u201d\u3002\u4f46\u662f\uff0c\u5047\u5982\u4f60\u60f3\u4eab\u53d7Smoluchowski\u65b9\u7a0b\u7684\u4fbf\u5229\u53bb\u63cf\u8ff0\u51dd\u80f6\u5316\u70b9\u4e4b\u524d\u7684\u52a8\u529b\u5b66\uff0c\u4f60\u76f8\u5f53\u4e8e\u5426\u5b9a\u4e86\u4f53\u7cfb\u662f\u4e00\u4e2a\u7269\u7406\u51dd\u80f6\uff08\u5bf9\u4e8e\u5438\u5f15\u529b\u8f83\u5f3a\u7684\u201c\u5f3a\u52a8\u529b\u5b66\u4f53\u7cfb\u201d\uff0c\u786e\u5b9e\u4e5f\u5e94\u8be5\u8fd1\u4f3c\u4e8e\u5316\u5b66\u51dd\u80f6\uff09\uff0c\u56e0\u6b64\u4f60\u4e0d\u80fd\u53c8\u8bf4\u51dd\u80f6\u5316\u70b9\u540e\u5b58\u5728\u4e00\u4e2a\u5f88\u5927\u7684\u677e\u5f1b\u65f6\u95f4\uff0c\u81f3\u5c11\u4f60\u8981\u627f\u8ba4\u4f53\u7cfb\u5df2\u7ecf\u7edd\u5bf9\u5730nonergodic\u4e86\u3002\u6240\u4ee5\u6211\u624d\u8981\u501f\u7528Krall\u7684\u7406\u8bba\uff0c\u53e6\u5916\u627e\u4e00\u4e2a\u52a8\u6001\u7ed3\u6784\u6765\u89e3\u91ca\u51dd\u80f6\u5316\u70b9\u540e\u5f97\u5230\u7684\u03c4\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":577,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/577","url_meta":{"origin":2406,"position":2},"title":"\u671f\u520a\u535a\u6587\uff1a\u6211\u5bfc\u5e08\u5173\u4e8e\u671f\u520a\u7684\u201c\u5356\u7a7a\u8c03\u201d\u7406\u8bba\u4ee5\u53ca\u6211\u7684\u6f14\u7ece","author":"Andrew","date":"2009\u5e7410\u670820\u65e5","format":false,"excerpt":"\u6700\u8fd1\u7ec4\u91cc\u4e00\u4e2a\u8eab\u5728\u56fd\u5916\u7684\u540c\u5b66\u4e4b\u524d\u6295Langmuir\u7684\u4e00\u7bc7\u4e1c\u897f\u53d1\u56de\u6765\u5ba1\u7a3f\u610f\u89c1\u4e86\uff0c\u6709\u4e00\u4e2a\u5173\u952e\u7684\u56fe\u7cbe\u5ea6\u4e0d\u591f\uff0c\u201c\u8fbe\u4e0d\u5230Langmuir\u7684\u8981\u6c42\u201d\u3002\u6211\u7b49\u5728\u56fd\u5185\u7684\u540c\u5b66\u9700\u8981\u5e2e\u4ed6\u91cd\u505a\u6d4b\u8bd5\u8865\u6570\u636e\u3002\u6211\u5bfc\u5e08\u8bf4\uff0c\u4eba\u5bb6\u5356\u8d35\u7684\u7a7a\u8c03\uff0c\u5176\u4ed6\u4e0d\u8bf4\uff0c\u4f46\u603b\u4e4b\u4e0d\u4f1a\u6709\u5f88\u5435\u7684\u3002\u4f60\u7684\u7a7a\u8c03\u5f88\u5435\uff0c\u867d\u7136\u4e5f\u662f\u7a7a\u8c03\uff0c\u4e5f\u6ca1\u9020\u5047\u6ca1\u4eba\u5077\u5de5\u51cf\u6599\uff0c\u4f46\u5c31\u662f\u4e0a\u4e0d\u4e86\u6863\u6b21\uff0c\u4e0d\u7b26\u5408\u56fd\u7f8e\u7684\u8981\u6c42\uff0c\u5c31\u4e0d\u80fd\u62ff\u5230\u56fd\u7f8e\u5356\uff0c\u53ea\u80fd\u5730\u644a\u4e0a\u5356\u3002\u201d\u6240\u4ee5\uff0c\u5982\u679c\u4f60\u4e70\u5f88\u5dee\u7684\u4eea\u5668\uff0c\u5b9e\u9a8c\u8981\u6c42\u4e00\u65e6\u7a0d\u9ad8\u4e00\u70b9\u6570\u636e\u5c31\u7cbe\u5ea6\u4e0d\u591f\uff0c\u4f60\u5c31\u603b\u662f\u53d1\u4e0d\u4e86\u9ad8\u6863\u6b21\u6587\u7ae0\u3002\u6240\u4ee5\uff0c\u4e70\u4ec0\u4e48\u4eea\u5668\u90fd\u82b1\u94b1\u4e70\u5927\u540d\u724c\u5f88\u5927\u7a0b\u5ea6\u4e0a\u662f\u8fd9\u65b9\u9762\u8003\u8651\u3002\u7136\u540e\uff0c\u6587\u7ae0\u6863\u6b21\u201c\u88ab\u5173\u8054\u201d\u5230\u4eba\u7684\u7ecf\u8d39\u5347\u8fc1\u5229\u76ca\uff0c\u56e0\u6b64\uff0c\u540d\u724c\u4eea\u5668\u5382\u5546\u5f53\u7136\u8981\u5356\u8d35\u4e00\u70b9\u513f\uff0c\u53cc\u8d62\u561b\uff01\u53c8\u6240\u4ee5\uff0c\u5982\u679c\u4e70\u4e86\u8d35\u4eea\u5668\uff0c\u8fd8\u53d1\u4e0d\u4e86\u4ec0\u4e48\u597d\u6587\u7ae0\uff0c\u90a3\u4f60\u5c31\u771f\u7684\u662f\u83dc\u7684n\u6b21\u65b9\uff01\u6240\u4ee5\uff0c\u4e3a\u4ec0\u4e48\u5f88\u5927\u4e00\u90e8\u5206\u725b\u7ec4\u7684\u4eea\u5668DIY\u7a0b\u5ea6\u5f88\u9ad8\u3002Commercial available\u7684\u4eea\u5668\u5c1a\u4e14\u6709\u94b1\u5c31\u80fd\u4e70\u5f97\u5230\uff0c\u8fd9\u4e9b\u725b\u7ec4\u751a\u81f3\u5728\u6d4b\u8bd5\u624b\u6bb5\u4e0a\u90fd\u9886\u5148\u4e86\uff0c\u6709\u4ece\u7406\u8bba\u4e0a\u5784\u65ad\u4e86\u65b0\u53d1\u73b0\u7684\u53ef\u80fd\uff0c\u6709\u53ef\u80fd\u4e0d\u725b\u5417\uff1f\u6240\u4ee5\u4e2d\u56fd\u7684\u7814\u7a76\u4eba\u5458\u5982\u679c\u53ea\u61c2\u4e70\u4eea\u5668\uff0c\u6309\u7167\u4eea\u5668\u8bf4\u660e\u4e66\u548c\u8f6f\u4ef6\u6240\u63d0\u4f9b\u7684\u529f\u80fd\u6309\u6309\u94ae\u64cd\u4f5c\uff0c\u662f\u6c38\u8fdc\u4e0d\u53ef\u80fd\u9886\u5148\u7684\u3002\u4e8b\u5b9e\u4e0a\u79d1\u7814\u4eea\u5668\u7684\u529f\u80fd\u90fd\u662f\u4ece\u4ee5\u5f80\u57fa\u7840\u7814\u7a76\u7684Idea\u4e2d\u63d0\u53d6\u51fa\u6765\u7684\u3002\u6709\u8fd9\u4e2a\u529f\u80fd\u5c31\u8bf4\u660e\u6709\u4eba\u8fd9\u4e48\u505a\u8fc7\u4e86\u3002\u4f60\u7528\u73b0\u6210\u529f\u80fd\uff0c\u4f60\u7684\u5b9e\u9a8c\u5c31\u9996\u5148\u4e0d\u53ef\u80fd\u5728\u65b9\u6cd5\u4e0a\u6709\u4ec0\u4e48\u65b0\u610f\uff0c\u5728\u53d1\u73b0\u4e0a\u7684\u65b0\u610f\u4e5f\u5f88\u6709\u9650\u2014\u2014\u4f60\u53ea\u4f1a\u53d1\u73b0\u90a3\u4e9b\u5df2\u6709\u65b9\u6cd5\u5e94\u8be5\u80fd\u53d1\u73b0\u7684\u4e1c\u897f\u3002\u5f88\u591a\u540c\u5b66\u8ba4\u4e3aGPC\u662f\u6d4b\u5206\u5b50\u91cf\u7684\uff0c\u52a8\u6001\u5149\u6563\u5c04\u662f\u6d4b\u7c92\u5f84\u7684\u3002\u6211\u5bfc\u5e08\u6781\u5176\u4e0d\u723d\u8fd9\u4e00\u70b9\u3002\u4e00\u5b9a\u8981\u8bb0\u4f4f\uff1aGPC\u662f\u6d4b\u6d41\u51fa\u65f6\u95f4\u7684\uff0c\u52a8\u6001\u5149\u6563\u5c04\u662f\u6d4b\u5149\u6563\u5c04\u7684\uff01\u2014\u2014\u52a0\u4e2a\u201c\u52a8\u6001\u201d\u53ea\u662f\u4ee3\u8868\u4e86\u6570\u636e\u6536\u96c6\u548c\u6570\u5b66\u5904\u7406\u65b9\u6cd5\u3002\u6d41\u53d8\u4eea\u662f\u6d4b\u5f62\u53d8\u548c\u8f6c\u77e9\u7684\uff01\u751a\u81f3\u8981\u8ba4\u8bc6\u5230\uff0c\u6240\u6709\u7528\u7535\uff0c\u8fde\u63a5\u7535\u8111\u7684\u4eea\u5668\u90fd\u662f\u6d4b\u7535\u6d41\u6216\u8005\u7535\u538b\u7684\uff01\u4e00\u53f0\u6d4b\u7535\u538b\u7684\u4e1c\u4e1c\u4f60\u600e\u4e48\u4f1a\u7b97\u51fa\u5206\u5b50\u91cf\uff1f\u4f60\u4e0d\u77e5\u9053\u4f60\u5e72\u561b\u7528\uff1f\u8fd8\u53d1\u6587\u7ae0\uff1f\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u770b\uff0c\u4e2d\u56fd\u7814\u7a76\u4eba\u5458\u7684\u6c34\u5e73\u9700\u8981\u63d0\u9ad8\u3002\u4f46\u662f\uff0c\u76ee\u524d\u6c34\u5e73\u5bf9\u4e8e\u53d1\u6587\u7ae0\u6765\u8bb2\u8c8c\u4f3c\u663e\u4e0d\u51fa\u4ec0\u4e48\u5fc5\u8981\u6027\u3002\u62ffGPC\u6d4b\u5206\u5b50\u91cf\u548c\u62ff\u52a8\u6001\u5149\u6563\u5c04\u6d4b\u7c92\u5f84\u597d\u50cf\u95ee\u9898\u90fd\u4e0d\u5927\u3002\u4f46\u662f\uff0c\u5982\u679c\u5bf9\u4e8e\u5ba1\u7a3f\u5de5\u4f5c\u6765\u8bf4\uff0c\u8fd9\u79cd\u6c34\u5e73\u5c31\u592a\u5dee\u4e86\uff01\u5982\u679c\u6211\u4eec\u7684\u4f5c\u8005\u603b\u662fGPC\u6d4b\u5206\u5b50\u91cf\uff0c\u5149\u6563\u5c04\u6d4b\u7c92\u5f84\uff0c\u5ba1\u7a3f\u4eba\u4e5f\u76f8\u4fe1GPC\u7684\u5206\u5b50\u91cf\uff0c\u5149\u6563\u5c04\u7684\u7c92\u5f84\u3002\u90a3\u6211\u4eec\u5c31\u7b97\u518d\u5fe0\u8bda\u5730\u6295\u4e2d\u6587\u671f\u520a\uff0c\u4e2d\u56fd\u4eba\u7684\u7814\u7a76\u6c38\u8fdc\u4e5f\u4e0d\u4f1a\u5165\u6d41\u3002\u4e0d\u8fc7\uff0c\u4e2d\u56fd\u79d1\u7814\u4eba\u5458\u7684\u5de5\u4f5c\u76ee\u7684\u663e\u7136\u4e0d\u662f\u4e3a\u4e86\u8ba9\u4e2d\u56fd\u4eba\u7684\u7814\u7a76\u5165\u6d41\u751a\u81f3\u4e00\u6d41\uff0c\u800c\u662f\u4e3a\u4e86\u751f\u8ba1\u3002\u53d1\u6587\u7ae0\u662f\u6c42\u4eba\u53d1\u5de5\u94b1\uff0c\u5ba1\u7a3f\u5ba1\u57fa\u91d1\u5c31\u662f\u770b\u4eba\u7ed9\u5de5\u94b1\u3002\u6574\u4e2a\u4e8b\u60c5\u5c31\u7b97\u4e0d\u8bf4\u662f\u201c\u6743\u94b1\u4ea4\u6613\u201d\uff08\u522b\u90a3\u4e48\u6124\u9752\uff09\uff0c\u4e5f\u4e3b\u8981\u662f\u4e00\u5806\u4e0b\u9762\u7684\u4eba\u4e3a\u4e86\u6ee1\u8db3\u56fd\u5bb6\u79d1\u7814\u5f3a\u56fd\u7684\u68a6\u60f3\u7cca\u5f04\u4e86\u4e8b\u3002\u4f60\u544a\u8bc9\u4ed6\u6c34\u5e73\u5dee\uff0c\u4ed6\u4e00\u70b9\u90fd\u4e0d\u7740\u6025\u3002\u6709\u4ec0\u4e48\u529e\u6cd5\uff1f\u6ca1\u6709\u597d\u7684\u5ba1\u7a3f\u4eba\uff0c\u6211\u4eec\u4e2d\u56fd\u5c31\u529e\u4e0d\u51fa\u201c\u56fd\u7f8e\u201d\uff0c\u201c\u597d\u7a7a\u8c03\u201d\u5c31\u4e0d\u4f1a\u653e\u4e2d\u6587\u671f\u520a\u91cc\u5356\uff0c\u5356\u7684\u53ea\u6709\u5f88\u5435\u7684\u7a7a\u8c03\u3002\u662f\u4e0d\u662f\u7a7a\u8c03\uff1f\u662f\u3002\u6709\u6ca1\u6709\u9020\u5047\u6284\u88ad\uff1f\u5c31\u5f53\u6ca1\u6709\u5427\u3002\u51e0\u6d41\uff1fn\u6d41\u3002\u6211\u603b\u89c9\u5f97\u5916\u56fd\u4eba\u662f\u5929\u751f\u613f\u610f\u7814\u7a76\u79d1\u5b66\u7684\uff0c\u4e2d\u56fd\u4eba\u662f\u88ab\u903c\u7684\u2014\u2014\u4e0d\u7136\u575a\u8239\u5229\u70ae\u5c31\u54c7\u54c7\u54c7\u6253\u8fc7\u6765\u4e86\u3002\u6240\u4ee5\u6211\u4eec\u5f88\u5f3a\u8c03\u201c\u79d1\u7814\u5f3a\u56fd\u201d\u561b\u3002\u4eba\u5bb6\u5f53\u7136\u4e5f\u63d0\u79d1\u7814\u5f3a\u56fd\uff0c\u56e0\u4e3a\u8fd9\u662f\u4e8b\u5b9e\u4e0a\u6709\u6548\u7684\u3002\u4f46\u4eba\u5bb6\u4e0d\u662f\u4e00\u5f00\u59cb\u5c31\u79d1\u7814\u5f3a\u56fd\u6765\u7740\u3002\u6211\u4eec\u662f\u6328\u5b8c\u6253\uff0c\u5e26\u7740\u5c48\u8fb1\u548c\u201c\u5d1b\u8d77\u201d\u7684\u68a6\u60f3\u5f15\u5165\u79d1\u5b66\u7684\uff0c\u4e8b\u5b9e\u4e0a\u5565\u80fd\u5f3a\u56fd\u54b1\u5c31\u5f15\u5165\u5565\uff0c\u673a\u4f1a\u4e3b\u4e49\u5f97\u5f88\u3002\u5f15\u5165\u79d1\u5b66\u5728\u4e3b\u89c2\u4e0a\u5e76\u4e0d\u662f\u4ec0\u4e48\u5fc5\u7136\u3002\u6211\u6709\u51e0\u5e74\u6691\u5047\u8fde\u7eed\u4e0b\u4e61\u4e49\u6559\uff0c\u53d1\u73b0\u5c71\u533a\u7684\u7a77\u5b69\u5b50\u786e\u5b9e\u5f88\u6e34\u671b\u5ff5\u4e66\uff0c\u4f46\u4ed6\u4eec\u662f\u4e3a\u4e86\u6539\u53d8\u547d\u8fd0\u3002\u6240\u4ee5\u4e00\u65e6\u793e\u4f1a\u591a\u5143\u5316\uff0c\u8bfb\u4e66\u4e0d\u5305\u5206\u914d\u4e4b\u540e\uff0c\u9a6c\u4e0a\u5c31\u76db\u884c\u201c\u8bfb\u4e66\u65e0\u7528\u8bba\u201d\u3002\u4ed6\u4eec\u5bf9\u5ff5\u4e66\uff0c\u4e00\u4f1a\u513f\u6e34\u671b\u5f97\u8ba9\u4f60\u5fc3\u75db\uff1b\u8f6c\u773c\u53c8\u9119\u5937\u5f97\u8ba9\u4f60\u5fc3\u5bd2\u3002\u6240\u4ee5\u6211\u4eec\u4e0b\u4e61\u7684\u4e49\u5de5\u4ece\u6765\u4e0d\u8ddf\u4ed6\u4eec\u8d2f\u8f93\u4ec0\u4e48\u201c\u6539\u53d8\u8d2b\u7a77\u3001\u6539\u53d8\u547d\u8fd0\u201d\u7684\u7834\u9053\u7406\u3002\u6211\u4eec\u53ea\u8bb2\u6709\u8da3\u7684\u77e5\u8bc6\uff0c\u7b2c\u4e8c\u8bfe\u5802\u3002\u8bfb\u4e66\u7684\u6e34\u671b\u672c\u5e94\u6765\u77e5\u8bc6\u7684\u9b45\u529b\u3002\u79d1\u5b66\u7814\u7a76\u4e5f\u4e00\u6837\u3002\u56e0\u6b64\u6211\u4eec\u56fd\u5bb6\u53ef\u4ee5\u8bf4\u662f\u79d1\u7814\u7a77\u56fd\uff0c\u6211\u4eec\u7684\u79d1\u7814\u4eba\u5458\u662f\u7a77\u5b69\u5b50\u3002\u4e00\u4f1a\u513f\u62b1\u7740\u201c\u6539\u53d8\u547d\u8fd0\u201d\u7684\u7406\u60f3\u72c2\u641e\uff1b\u4e00\u4f1a\u513f\u53c8\u76db\u884c\u201c\u79d1\u5b66\u65e0\u7528\u8bba\u201d\uff0c\u5e26\u7740\u865a\u65e0\u4e3b\u4e49\u6df7\u996d\u5403\uff0c\u6284\u88ad\u527d\u7a83\u5076\u5c14\u4e3a\u4e4b\u3002\u8fd9\u5c31\u662f\u7a77\uff01\u522b\u4ee5\u4e3a\u82b1\u5f97\u8d77\u94b1\u4e70\u52a8\u6001\u5149\u6563\u5c04\u4f60\u5c31\u5f88\u5bcc\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":7551,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/7551","url_meta":{"origin":2406,"position":3},"title":"\u600e\u6837\u4ece\u6587\u732e\u7684\u5149\u6563\u5c04\u6570\u636e\u4f30\u7b97\u5f53\u524d\u9ad8\u5206\u5b50\u6eb6\u6db2\u5c3a\u5bf8\uff1f","author":"Andrew","date":"2017\u5e7412\u670812\u65e5","format":false,"excerpt":"[latexpage] \u6211\u4eec\u7ecf\u5e38\u9047\u5230\u4e0d\u60f3\u81ea\u5df1\u505a\u5149\u6563\u5c04\u5c31\u60f3\u83b7\u5f97\u5f53\u524d\u6837\u54c1\u7684\u5206\u5b50\u91cf\u548c\u6eb6\u6db2\u7684\u5206\u5b50\u5c3a\u5bf8\u4fe1\u606f\u7684\u60c5\u51b5\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u5f88\u591a\u5929\u7136\u9ad8\u5206\u5b50\uff0c\u4e70\u56de\u6765\u662f\u4e0d\u77e5\u9053\u5206\u5b50\u91cf\u7684\u3002\u5149\u6563\u5c04\u4eea\u6216\u751a\u81f3\u662fSEC-MALLS\u4e0d\u662f\u5f88\u5bb9\u6613\u5177\u5907\u7684\u6761\u4ef6\uff0c\u4f46\u662f\u6d4b\u91cf\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]$\u5c31\u57fa\u672c\u8c01\u90fd\u80fd\u505a\u3002\u6240\u4ee5\u5f88\u81ea\u7136\u662f\u5e0c\u671b\u80fd\u901a\u8fc7\u62a5\u5bfc\u7684Mark\u2014Houwink\u5173\u7cfb$\\left[\\eta\\right]\\sim M^a$\u6765\u4f30\u7b97\u5206\u5b50\u91cf\u3002\u6587\u732e\u7684Mark\u2014Houwink\u5173\u7cfb\u4e00\u822c\u662f\u901a\u8fc7\u5bf9\u4e0d\u540c\u5206\u5b50\u91cf\u7684\u5355\u5206\u6563\u6837\u54c1\u540c\u65f6\u6d4b\u91cf\u7279\u6027\u7c98\u6570\u548c\u7edd\u5bf9\u5e73\u5747\u5206\u5b50\u91cf\uff08\u4f8b\u5982\u6e17\u900f\u538b\u5f97\u5230\u7684\u6570\u5747\u5206\u5b50\u91cf\u6216\u8005\u5149\u6563\u5c04\u5f97\u5230\u7684\u91cd\u5747\u5206\u5b50\u91cf\uff09\u6765\u7ed9\u51fa\u7684\u3002\u5f53\u7136\uff0c\u771f\u6b63\u7684\u5355\u5206\u6563\u6837\u54c1\u53ef\u4ee5\u5f53\u4f5c\u6570\u5747\u4e0e\u91cd\u5747\u65e0\u5dee\u522b\u3002\u6587\u732e\u62a5\u5bfc\u7684Mark\u2014Houwink\u5173\u7cfb\u90fd\u662f\u5728\u7279\u5b9a\u6eb6\u5242\u548c\u6e29\u5ea6\u6761\u4ef6\u4e0b\u7684\u3002\u4f60\u4e3a\u4e86\u83b7\u5f97\u5206\u5b50\u91cf\uff0c\u53ef\u4ee5\u5728\u76f8\u5e94\u7684\u6761\u4ef6\u4e0b\u6d4b\u8bd5\u5f53\u524d\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570\u7136\u540e\u5e94\u7528\u6587\u732e\u7684Mark\u2014Houwink\u53c2\u6570\u3002\u4f46\u4f60\u66f4\u9700\u8981\u7684\u5f80\u5f80\u662f\u53e6\u4e00\u79cd\u4efb\u610f\u6eb6\u5242\u6216\u6e29\u5ea6\u4e0b\u7684\u5206\u5b50\u5c3a\u5bf8\u3002\u5149\u77e5\u9053\u5206\u5b50\u91cf\u4e0d\u591f\uff0c\u8fd8\u8981\u77e5\u9053\u6269\u5f20\u6bd4$\\alpha$\u3001Flory\u6307\u6570$\\nu$\u7b49\u3002\u66f4\u9ebb\u70e6\u7684\u662f\uff0c\u627e\u4e0d\u5230Mark\u2014Houwink\u5173\u7cfb\u7684\u62a5\u9053\uff0c\u53ea\u627e\u5230\u5bf9\u5355\u4e2a\u6837\u54c1\u505a\u7684\u5149\u6563\u5c04\u6570\u636e\u3002\u8fd9\u65f6\u5c31\u9700\u8981\u57fa\u4e8e\u666e\u904d\u63a5\u53d7\u7684\uff08\u4ea6\u5373\u5ba1\u7a3f\u4eba\u4e00\u822c\u4e0d\u8d28\u7591\u7684\uff09\u9ad8\u5206\u5b50\u6eb6\u6db2\u7406\u8bba\u6765\u4ece\u8fd9\u4e9b\u6587\u732e\u6570\u636e\u4f30\u7b97\u5f53\u524d\u6761\u4ef6\u4e0b\u7684\u5206\u5b50\u5c3a\u5bf8\u3002 \u4e3a\u4e86\u6e05\u6670\uff0c\u6211\u4eec\u628a\u805a\u5408\u7269\u79cd\u7c7b\u7528\u5927\u5199\u82f1\u6587\u5b57\u6bcdA\u3001B\u6765\u8868\u793a\uff0c\u628a\u4e00\u5b9a\u7684\u6eb6\u5242\u548c\u6e29\u5ea6\u6761\u4ef6\u7528\u5e0c\u814a\u5b57\u6bcd\u03b8\u3001\u03b1\u3001\u03b2\u6765\u8868\u793a\uff0c\u5176\u4e2d\u03b8\u8868\u793a\u65e0\u6270\u6761\u4ef6\u3002\u8fd9\u4e9b\u90fd\u53ea\u4f1a\u7528\u4f5c\u4e0b\u6807\u3002\u4e0d\u968f\u6761\u4ef6\u53d8\u5316\u7684\u91cf\u4e0d\u6807\u5e0c\u814a\u5b57\u6bcd\u4e0b\u6807\u3002\u4e3a\u4e86\u8fdb\u4e00\u6b65\u7b80\u5316\uff0c\u5f53\u524d\u5173\u5fc3\u7684\u805a\u5408\u7269\uff0c\u5c31\u4e0d\u6807\u5b57\u6bcdA\u4e86\uff0c\u53e6\u4e00\u79cd\u805a\u5408\u7269\u624d\u4f1a\u6807B\u3002\u4f8b\u5982$\\alpha_\\alpha$\u8868\u793a\u5f53\u524d\u5173\u5fc3\u7684\u805a\u5408\u7269\u5728\u7b2c\u4e00\u79cd\u6761\u4ef6\u4e0b\uff08\u6761\u4ef6\u03b1\uff09\u7684\u6269\u5f20\u7cfb\u6570\u3002\u5c31\u7b97\u662f\u5f53\u524d\u5173\u5fc3\u7684\u9ad8\u5206\u5b50\uff0c\u6587\u732e\u4f7f\u7528\u7684\u5206\u5b50\u91cf\u8ddf\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5206\u5b50\u91cf\u662f\u4e0d\u4e00\u6837\u7684\uff0c\u6211\u4eec\u6700\u7ec8\u662f\u8981\u77e5\u9053\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u7684\u5206\u5b50\u91cf\u3002\u4e8e\u662f\uff0c\u7528\u4e00\u4e2aprime\u6765\u8868\u793a\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u3002\u4f8b\u5982$M^\\prime$\u662f\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u7684\u5206\u5b50\u91cf\uff0c$\\left[\\eta\\right]^\\prime_{\\beta}$\u662f\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u5728\u03b2\u6761\u4ef6\u4e0b\u7684\u7279\u6027\u7c98\u6570\u3002 \u9996\u5148\u9700\u8981\u4f30\u7b97\u8fd9\u79cd\u805a\u5408\u7269\u7684\u5355\u4f4d\u94fe\u957f\u8d28\u91cf$M_1$\u6216\u8005\u91cd\u590d\u5355\u5143\u957f\u5ea6$l_1$\u3002\u5b83\u4eec\u4e4b\u95f4\u6709\u5173\u7cfb$M_1=M_0\/l_1$\uff0c\u5176\u4e2d$M_0$\u662f\u91cd\u590d\u5355\u539f\u7684\u8d28\u91cf\u3002$l_1$\u4e00\u822c\u662f\u6839\u636e\u91cd\u590d\u5355\u5143\u7684\u952e\u957f\u952e\u89d2\u7b49\u51e0\u4f55\u4fe1\u606f\u4f30\u7b97\u7684\u3002\u4e0d\u7ba1\u600e\u4e48\u53bb\u4f30\u7b97\uff0c\u6700\u540e\u8981\u7528\u7684\u662f$M_1$\u3002\u4e00\u822c\u6587\u732e\u91cc\u4f1a\u6709\u4f30\u7b97\u7684\uff0c\u4e0d\u7528\u81ea\u5df1\u505a\u3002 \u4e00\u822c\u80fd\u67e5\u5230\u7684\u5149\u6563\u5c04\u5de5\u4f5c\uff0c\u90fd\u662f\u5728\u67d0\u6eb6\u5242\u548c\u6e29\u5ea6\u4e0b\uff08\u8bb0\u4e3a\u6761\u4ef6\u03b1\uff09\u505a\u4e00\u4e2aZimm\u56fe\uff0c\u53ef\u4ee5\u5f97\u5230\u6837\u54c1\u7684\uff08\u91cd\u5747\uff09\u5206\u5b50\u91cf$M$\u3001\u7b2c\u4e8c\u7ef4\u5229\u7cfb\u6570$A_{2,\\alpha)$\u548c\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle_\\alpha$\u3002\u5c31\u7b97\u8bba\u6587\u7684\u6b63\u6587\u6ca1\u6709\u7ed9\u51fa\u503c\uff0c\u53ea\u8981\u7ed9\u4e86\u6570\u636e\u56fe\uff0c\u4f60\u81ea\u5df1\u4e5f\u53ef\u4ee5\u4ece\u56fe\u4e2d\u5f97\u5230\u3002\u8fd9\u90e8\u5206\u7684\u539f\u7406\u6bd4\u8f83\u57fa\u672c\uff0c\u4e00\u822c\u7684\u9ad8\u5206\u5b50\u6eb6\u6db2\u7406\u8bba\u7684\u4e66\u7684\u8bb2\u8ff0\u4e0d\u4f1a\u6709\u4ec0\u4e48\u4ee4\u4eba\u56f0\u60d1\u7684\u5dee\u5f02\uff0c\u5c31\u4e0d\u5728\u6b64\u89e3\u91ca\u4e86\u3002\u5982\u679c\u627e\u5230\u6587\u732e\u505a\u4e86\u4e0d\u6b62\u4e00\u4e2a\u5206\u5b50\u91cf\u7684\u6837\u54c1\uff0c\u4f46\u662f\u6ca1\u6709\u6d4b\u5b83\u4eec\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\alpha$\u56e0\u6b64\u8fd8\u662f\u4e0d\u77e5\u9053Mark\u2014Houwink\u7cfb\u6570\uff0c\u90a3\u4f60\u4ecd\u7136\u53ef\u4ee5\u65b9\u4fbf\u5730\u6839\u636e$\\left\\langle S^2\\right\\rangle^{1\/2}_\\alpha\\sim M^{\\nu_\\alpha}$\u5f97\u5230\u6587\u732e\u6761\u4ef6\u4e0b\u7684$\\nu_\\alpha$\uff08\u54ea\u6015\u6587\u732e\u6ca1\u505a\u4f60\u4e5f\u53ef\u4ee5\u7528\u5b83\u7684\u6570\u636e\u81ea\u5df1\u505a\uff0c\u8fd9\u4e00\u70b9\u5728\u4e0b\u6587\u4e2d\u5c31\u4e0d\u518d\u91cd\u590d\u63d0\u793a\u4e86\uff09\u3002 \u5982\u679c\u6587\u732e\u53ea\u505a\u4e86\u4e00\u4e2a\u5206\u5b50\u91cf\u7684\u6837\u54c1\uff0c\u81f3\u5c11\u4e5f\u5df2\u7ecf\u6709$M$\u548c$A_2$\u4e86\u3002\u8fd9\u65f6\u53ef\u4ee5\u901a\u8fc7\u6269\u5f20\u7cfb\u6570\u6765\u6c42Flory\u6307\u6570\u3002\u5982\u679c\u6269\u5f20\u7cfb\u6570\u662f\u5173\u4e8e\u5747\u65b9\u672b\u7aef\u8ddd\u7684\uff0c\u5c31\u6709\uff1a$\\alpha_\\alpha=\\left\\langle h^2\\right\\rangle^{1\/2}_\\alpha\/\\left\\langle h^2\\right\\rangle_\\theta^{1\/2}$\uff0c\u5176\u4e2d\uff0c$\\left\\langle h^2\\right\\rangle^{1\/2} = b_\\alpha N_\\alpha^\\nu_\\alpha$\uff0c$\\left\\langle h^2\\right\\rangle_\\theta^{1\/2} = b_\\alpha N_\\alpha^{1\/2}$\uff0c$b_\\alpha$\u662fKuhn\u94fe\u6bb5\u957f\u5ea6\uff0c$N_\\alpha$\u662fKuhn\u94fe\u6bb5\u7684\u4e2a\u6570\u3002$N_\\alpha=M\/\\left(M_1 b_\\alpha\\right)$\u3002\u90a3\u4e48\u5c31\u53ef\u4ee5\u7531\u6269\u5f20\u7cfb\u6570\u8ba1\u7b97Flory\u6307\u6570\u4e86\uff0c\u6240\u7f3a\u7684\u53c2\u6570\u662f$\\alpha_\\alpha$\u548c$b_alpha$\u3002 $b_\\alpha$\u4e5f\u662f\u8981\u627e\u6587\u732e\u7684\u3002\u6587\u732e\u4e00\u822c\u6709\u4e24\u79cd\u505a\u6cd5\uff1a\u4e00\u662f\u5149\u6563\u5c04\u5f97\u5230\u4e86\u6bd4\u8f83\u5bbd\u6ce2\u77e2\u8303\u56f4\u7684form factor\uff0c\u53ef\u4ee5\u770b\u5230coil\u884c\u4e3a\u5411rod\u884c\u4e3a\u7684\u8f6c\u53d8\uff0c\u8fd9\u4e2a\u8f6c\u53d8\u6240\u5bf9\u5e94\u7684\u5c3a\u5ea6\u5c31\u662f$b$\u3002\u4e8c\u662f\u901a\u8fc7\u4e00\u4e9b\u542b\u6709\u6301\u7eed\u957f\u5ea6$l_\\mathrm{p}$\u53c2\u6570\u7684\u94fe\u6a21\u578b\u6765\u62df\u5408\u6d4b\u5f97\u7684$\\left\\langle S^2\\right\\rangle$\u6570\u636e\u5f97\u5230$l_\\mathrm{p}$\u4ece\u800c\u5f97\u5230$b$\u3002\u4e0d\u7ba1\u600e\u4e48\u6837\u4f60\u8981\u67e5\u5230\u8fd9\u4e2a\u6570\u636e\u3002\u7531\u4e8e$b_\\alpha$\u7684\u503c\u662f\u4f9d\u8d56\u6761\u4ef6\uff0c\u6240\u4ee5\u6700\u597d\u662f\u540c\u4e00\u4e2a\u62a5\u9053\u91cc\u4e0d\u4ec5\u4f5c\u4e86Zimm\u56fe\uff0c\u8fd8\u628a\u5149\u5f3a\u548c\u6ce2\u77e2\u66f2\u7ebf\u7ed9\u51fa\u6765\uff0c\u7136\u540e\u4f9b\u4f60\u7528\u7b2c\u4e00\u79cd\u65b9\u6cd5\u4f30\u7b97\u51fa$b$\u3002\u6587\u732e\u81ea\u5df1\u628a\u8fd9\u4ef6\u4e8b\u505a\u4e86\u7684\u8bdd\u5c31\u66f4\u597d\u4e86\u3002 \u81f3\u4e8e\u6269\u5f20\u7cfb\u6570\uff0c\u662f\u8fd9\u6837\u5f97\u5230\u7684\uff1a\u901a\u8fc7\u6bd4\u8f83\u53e6\u4e00\u79cd\u9ad8\u5206\u5b50B\u7684$M_\\mathrm{B}$\u3001$A_{2,\\mathrm{B}}$\u548c\u6269\u5f20\u7cfb\u6570$\\alpha_{B\\beta}$\u6765\u4f30\u7b97\u5f53\u524d\u7684\u9ad8\u5206\u5b50\u5728\u6761\u4ef6\u03b1\u7684\u6269\u5f20\u7cfb\u6570$\\alpha_\\alpha$\u3002\u5177\u4f53\u5730\u8bb2\uff0c\u4f60\u9700\u8981\u67e5\u627e\u53e6\u4e00\u79cd\u7814\u7a76\u5f97\u6bd4\u8f83\u591a\u7684\u9ad8\u5206\u5b50B\u7684\u6570\u636e\uff0c\u8fd9\u6837\u5c31\u6709\u671b\u627e\u5230\u540c\u65f6\u62a5\u9053\u4e86\u5176\u5206\u5b50\u91cf$M_\\mathrm{B}$\u548c\u67d0\u6761\u4ef6\uff08\u8bb0\u4e3a\u03b2\uff09\u4e0b\u7684$A_{2,\\mathrm{B}}$\u548c\u6269\u5f20\u6bd4$\\alpha_\\mathrm{B\\beta}$\u7684\u6587\u732e\u3002\u7136\u540e\uff0c\u6839\u636eFlory\u7684\u6269\u5f20\u7cfb\u6570\u5173\u7cfb\u5f0f$\\alpha^5-\\alpha^3=2C_\\mathrm{M}\\psi\\left(1-\\Theta\/T\\right)M^{1\/2}$\u53ef\u77e5\uff0c\u4e0d\u540c\u9ad8\u5206\u5b50\u5728\u540c\u4e00\u7b2c\u4e8c\u7ef4\u5229\u7cfb\u6570\u4e0b\u7684$\\left(\\alpha^5-\\alpha^3\\right)\/M^{1\/2}$\u503c\u662f\u5dee\u522b\u5f88\u5c0f\u7684\u3002\u4e8e\u662f\u4f60\u5c31\u53ef\u4ee5\u901a\u8fc7$\\frac{\\alpha_\\alpha^5-\\alpha_\\alpha^3}{M^{1\/2}}=\\frac{\\alpha_\\mathrm{B\\beta}^5-\\alpha_\\mathrm{B\\beta}^3}{M_\\mathrm{B}^{1\/2}}$\u6765\u8ba1\u7b97\u4f60\u8981\u7684\u6269\u5f20\u7cfb\u6570$\\alpha_\\alpha$\u4e86\u3002\u6709\u4e86$\\alpha_\\alpha$\u548c$b_\\alpha$\uff0c\u5c31\u53ef\u4ee5\u6c42$\\nu_\\alpha$\u4e86\u3002 \u77e5\u9053\u4e86$\\nu_\\alpha$\uff0c\u4e0b\u4e00\u6b65\u5c31\u662f\u8ba1\u7b97\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u7684\u5206\u5b50\u91cf$M^\\prime$\u3002\u8fd9\u65f6\u5c31\u9700\u8981\u4f7f\u7528\u7279\u6027\u7c98\u6570\u7684\u6570\u636e\u4e86\u3002\u4f60\u9700\u8981\u518d\u4ece\u6587\u732e\u4e2d\u627e\u5230\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\alpha$\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u4ece\u6587\u732e\u4e2d\u4e00\u5171\u8981\u627e\u5230\u5bf9\u67d0\u5206\u5b50\u91cf\u4e3a$M$\u7684\u6837\u54c1\u5728\u540c\u4e00\u6761\u4ef6\u03b1\u4e0b\u7684\uff1a$b_\\alpha$\u548c$\\left[\\eta\\right]_\\alpha$\uff0c\u6309\u4e0a\u8ff0\u7684\u8ba1\u7b97\u65b9\u6cd5\u7b97\u51fa$\\nu_\\alpha$\u3002\u540c\u65f6\uff0c\u4f60\u624b\u5934\u4e0a\u7684\u6837\u54c1\u4e5f\u8981\u81ea\u5df1\u62ff\u53bb\u5728\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\u6d4b\u7279\u6027\u7c98\u6570\uff0c\u5f97\u5230$\\left[\\eta\\right]^\\prime_\\alpha$\u3002\u8fd9\u65f6\u6839\u636eFlory\u2014Fox\u5173\u7cfb\u6709$\\left[\\eta\\right]_\\alpha\/\\left[\\eta\\right]^\\prime_\\alpha=\\left(M\/M^\\prime\\right)^{\\left(3\\nu_\\alpha-1\\right)}$\uff0c\u4ece\u800c\u5f97\u5230\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5206\u5b50\u91cf$M^\\prime$\u3002 \u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u5982\u679c\u8981\u4f30\u7b97\u53e6\u4e00\u79cd\u6eb6\u5242\u6216\u6e29\u5ea6\u6761\u4ef6\uff08\u8bb0\u4e3a\u03b3\uff09\u4e0b\u7684\u5404\u79cd\u5c3a\u5bf8\uff0c\u5c31\u5fc5\u987b\u77e5\u9053\u65b0\u6761\u4ef6\u4e0b\u8fd9\u4e00\u9ad8\u5206\u5b50\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\gamma$\u548c\u5206\u5b50\u91cf$M$\uff0c\u8fd9\u540c\u6837\u8981\u4ece\u6587\u732e\u91cc\u627e\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u5c31\u662f\u4f60\u60f3\u83b7\u5f97\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u6761\u4ef6\u03b3\u7684\u4fe1\u606f\uff0c\u4f60\u5c31\u8981\u627e\u5230\u6709\u4eba\u4e5f\u5728\u6761\u4ef6\u03b3\u4e0b\u505a\u8fc7\u540c\u79cd\u9ad8\u5206\u5b50\u7684\u5b9e\u9a8c\uff0c\u5426\u5219\u5c31\u6ca1\u620f\u4e86\u3002\u5982\u679c\u6709\uff0c\u90a3\u4f60\u53ea\u9700\u8981\u518d\u5728\u6761\u4ef6\u03b3\u4e0b\u6d4b\u4e00\u6b21\u624b\u5934\u4e0a\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]^\\prime_\\gamma$\uff0c\u5c31\u53ef\u4ee5\u7c7b\u4f3c\u5730\u7528\u5173\u7cfb$\\left[\\eta\\right]_\\gamma\/\\left[\\eta\\right]^\\prime_\\gamma=\\left(M\/M^\\prime\\right)^{\\left(3\\nu_\\gamma-1\\right)}$\u5f97\u5230\u65b0\u6761\u4ef6\u7684Flory\u6307\u6570\u3002\u7136\u540e\u53ef\u4ee5\u5229\u7528Flory\u2014Fox\u5173\u7cfb\u672c\u8eab\u5f97\u5230\u65b0\u6761\u4ef6\u4e0b\u7684Kuhn\u94fe\u6bb5\u6570\u91cf$N^\\prime_\\gamma$\u548c\u957f\u5ea6$b_\\gamma$\uff0c\u8fdb\u800c\u5f97\u5230\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle_\\gamma^\\prime$\u3002 \u6eb6\u80c0\u94fe\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^{1\/2}$\u4e0e\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle^{1\/2}$\u4e4b\u95f4\u6ca1\u6709\u7b80\u5355\u7684\u7cbe\u786e\u5173\u7cfb\u3002\u4f46\u4ecd\u7136\u53ef\u4ee5\u6309\u6587\u672b\u5173\u4e8e\u6269\u5f20\u7cfb\u6570\u7684\u8865\u5145\u8bf4\u660e\u53ef\u4ee5\u4f5c\u6b64\u6362\u7b97\uff0c\u5f97\u5230\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^\\prime_\\gamma$\u3002\u6709\u4e86\u5747\u65b9\u56de\u8f6c\u534a\u5f84\uff0c\u4f60\u5c31\u53ef\u4ee5\u8ba1\u7b97\u65b0\u6761\u4ef6\u4e0b\u5f53\u524d\u6837\u54c1\u7684\u5f88\u591a\u4fe1\u606f\uff0c\u4f8b\u5982\u534a\u6d53\u6eb6\u6db2\u7684\u63a5\u89e6\u6d53\u5ea6$c^*=3M\/\\left(4\\pi N_\\mathrm{A}\\left\\langle S^2\\right\\rangle^{1\/2}\\right)$\uff0c\u4ee5\u53ca\u76f8\u5173\u957f\u5ea6\uff08blob size\uff09$\\xi=\\left\\langle S^2\\right\\rangle^{1\/2}\\left(c\/c^*\\right)^{-\\nu\/\\left(3\\nu-1\\right)}$\u3002\u6ce8\u610f\u5f0f\u4e2d\u4f9d\u8d56\u6761\u4ef6\u7684\u91cf\u8981\u53d6\u540c\u4e00\u6761\u4ef6\u4e0b\u7684\u503c\u3002 \u5bf9\u4e8e\u9ad8\u5206\u5b50\u6eb6\u6db2\u4ea4\u8054\u5f62\u6210\u7684\u51dd\u80f6\uff0c\u4e5f\u53ef\u4ee5\u5728\u540c\u6837\u7684\u6eb6\u5242\u548c\u6e29\u5ea6\uff08\u5982\u6761\u4ef6\u03b3\uff0c\u4e0d\u518d\u6807\u793a\u4e86\uff09\u4e0b\u6d4b\u91cf\u5e73\u53f0\u6a21\u91cf$G_\\mathrm{p}$\uff0c\u7136\u540e\u7528Nijenhuis\u7684\u5f0f\u5b50\uff0c\u5f97\u5230\u4ea4\u8054\u70b9\u95f4\u5206\u5b50\u91cf$M_\\mathrm{c}$\u3002 \\begin{equation}G_\\mathrm{p}=\\frac{2cRT}{M}\\left(\\frac{M}{M_\\mathrm{c}}\\frac{f-1}{f}-1\\right)\\left(1-w_\\mathrm{s}\\right)\\end{equation}\\begin{equation}\\frac{M}{M_\\mathrm{c}}=-\\frac{\\mathrm{ln}w_\\mathrm{s}}{1-w_\\mathrm{s}}\\frac{1-w_\\mathrm{s}^{0.5f}}{1-w_\\mathrm{s}^{0.5f-1}}\\end{equation} $M$\u662f\u9ad8\u5206\u5b50\u7684\u5206\u5b50\u91cf\uff0c$c$\u662f\u9ad8\u5206\u5b50\u6d53\u5ea6\uff08\u5355\u4f4d\u4f53\u79ef\u7684\u9ad8\u5206\u5b50\u8d28\u91cf\uff09\u3002$f$\u662f\u4ea4\u8054\u70b9\u7684\u5b98\u80fd\u5ea6\uff0c$w_\\mathrm{s}$\u662f\u51dd\u80f6\u4e2d\u7684sol fraction\u3002 \u5f97\u5230\u4e86\u4ea4\u8054\u70b9\u95f4\u5e73\u5747\u5206\u5b50\u91cf\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u4e4b\u524d\u5f97\u5230\u7684\u540c\u6837\u6761\u4ef6\u4e0b\u7684\u6837\u54c1\u7684$M$\u3001$M_1$\u3001$\\nu$\u3001$b$\u8ba1\u7b97\u4ea4\u8054\u70b9\u95f4\u5e73\u5747Kuhn\u94fe\u6bb5\u6570$N_\\mathrm{c}$\uff0c\u8fdb\u800c\u5047\u8bbe\u7f51\u773c\u5c3a\u5bf8\u8fd1\u4f3c\u7b49\u4e8e\u4ea4\u8054\u70b9\u95f4\u94fe\u6bb5\u7684\u5747\u65b9\u672b\u7aef\u8ddd\uff0c\u53ef\u5f97\u7f51\u773c\u5c3a\u5bf8$\\xi=bN_\\mathrm{c}^\\nu$\u3002 \u529f\u80fd\u6027\u6c34\u51dd\u80f6\u7684\u6eb6\u5242\u6761\u4ef6\u5343\u53d8\u4e07\u5316\u3002\u6e29\u5ea6\u4f9d\u8d56\u6027\u5c1a\u4e14\u6709\u70ed\u529b\u5b66\u4e00\u822c\u5173\u7cfb\u53ef\u4f9d\u8d56\uff0c\u4f46\u662f\u4e0d\u540cpH\u6216\u76d0\u7684\u79cd\u7c7b\u3001\u6d53\u5ea6\uff0c\u4e0d\u53ef\u80fd\u90fd\u6709\u4eba\u505a\u8fc7\u5149\u6563\u5c04\u5b9e\u9a8c\u3002\u54ea\u6015\u81ea\u5df1\u6709\u5149\u6563\u5c04\uff0c\u4e5f\u4e0d\u53ef\u80fd\u53d8\u4e00\u4e0b\u76d0\u6d53\u5ea6\u5c31\u6d4b\u4e00\u6b21\u6216\u8005\u641e\u51fa\u4ec0\u4e48\u5de5\u4f5c\u66f2\u7ebf\u6765\u3002\u8fd9\u65f6\u6211\u4eec\u8981\u6709\u4e00\u79cd\u4e0d\u90a3\u4e48\u7ea0\u7ed3\u7684\u65b9\u5f0f\u3002\u5728\u5904\u7406\u8fd9\u79cd\u95ee\u9898\u7684\u65f6\u5019\uff0c\u53ea\u80fd\u628a\u6761\u4ef6\u4f9d\u8d56\u7684\u53c2\u6570\u90fd\u5f53\u4f5c\u53d8\u91cf\uff0c\u770b\u80fd\u4e0d\u80fd\u641e\u4e00\u4e9b\u62df\u5408\u4e86\u3002 \u5173\u4e8e\u6269\u5f20\u7cfb\u6570\u7684\u8865\u5145\u8bf4\u660e \u524d\u9762\u63d0\u5230\u5bf9\u4e8e\u6eb6\u80c0\u94fe\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^{1\/2}$\u4e0e\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle^{1\/2}$\u4e4b\u95f4\u6ca1\u6709\u7b80\u5355\u7684\u7cbe\u786e\u5173\u7cfb\uff0c\u6269\u5f20\u7cfb\u6570\u4e5f\u9700\u8981\u5206\u5f00\u5b9a\u4e49\u3002\u5747\u65b9\u672b\u7aef\u8ddd\u7684\u6269\u5f20\u7cfb\u6570\u662f$\\alpha_h\\equiv\\left\\langle h^2\\right\\rangle^{1\/2}\/\\left\\langle h^2\\right\\rangle_\\mathrm{\\theta} ^{1\/2}$\uff1b\u5747\u65b9\u56de\u8f6c\u534a\u5f84\u7684\u6269\u5f20\u7cfb\u6570\u662f$\\alpha_S\\equiv\\left\\langle S^2\\right\\rangle^{1\/2}\/\\left\\langle\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2498,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/2498","url_meta":{"origin":2406,"position":4},"title":"\u6587\u7ae0\u7684Discussion\u90e8\u5206","author":"Andrew","date":"2011\u5e743\u670813\u65e5","format":false,"excerpt":"\u6458\u8981\uff1a\u6eb6\u89e3\u5728\u80f6\u4f53\u60ac\u6d6e\u6db2\u4e2d\u7684\u805a\u5408\u7269\uff0c\u5982\u679c\u5438\u9644\u5728\u80f6\u4f53\u7c92\u5b50\u7684\u8868\u9762\uff0c\u7531\u4e8e\u589e\u52a0\u4e86\u65a5\u529b\u7684\u4f5c\u7528\u8ddd\u79bb\uff0c\u63d0\u9ad8\u4e86\u7c92\u5b50\u95f4\u4f5c\u7528\u52bf\u5792Umax\uff0c\u7c92\u5b50\u805a\u96c6\u901f\u7387\u4f1a\u964d\u4f4e\u3002\u8fd9\u662f\u5b9a\u6027\u7684\u89e3\u91ca\u3002\u672c\u5b9e\u9a8c\u65e2\u7136\u80fd\u5f97\u5230\u5e73\u79fb\u56e0\u5b50\u968f\u805a\u5408\u7269\u6d53\u5ea6\u7684\u53d8\u5316\u5173\u7cfb\uff0c\u5c31\u60f3\u534a\u5b9a\u91cf\u5730\u89e3\u91ca\u4e00\u4e0b\u3002\u805a\u5408\u7269\u5438\u9644\u5728\u7c92\u5b50\u4e0a\u7684\u4f4d\u963b\u52bf\u51fd\u6570\u5df2\u7ecf\u6709\u6210\u719f\u7684\u7406\u8bba\u6a21\u578b\u3002\u7c92\u5b50\u805a\u96c6\u901f\u7387\u4e0e\u4f5c\u7528\u52bf\u5792\u4e4b\u95f4\u7684\u5173\u7cfb\u4e5f\u53ef\u4ee5\u901a\u8fc7Smoluchowski\u65b9\u7a0b\u548cstability ratio\u6765\u63cf\u8ff0\u3002\u96be\u70b9\u5728\u4e8e\u8bf4\u660e\u4e24\u4e2a\u5173\u7cfb\uff1a\u4e00\u662f\u5e73\u79fb\u56e0\u5b50\u4e0eUmax\u7684\u5173\u7cfb\uff0c\u4e8c\u662f\u8981\u4ece\u7c92\u5b50\u7684\u603b\u52bf\u80fd\u51fd\u6570U=U\u8303+U\u7535+U\u805a\u5408\u7269\u7684\u8868\u8fbe\u5f0f\u6c42\u6781\u5927\u503c\uff0c\u83b7\u5f97Umax\u4e0e\u805a\u5408\u7269\u5438\u9644\u91cf\u0393\u6216\u6dfb\u52a0\u91cfcp\u7684\u5173\u7cfb\u3002\u4ee5\u4e0b\u662f\u6211\u67e5\u9605\u8d44\u6599\u540e\u7684\u603b\u7ed3\uff0c\u611f\u89c9\u6ca1\u6709\u80fd\u529b\u518d\u5b8c\u5584\u4e86\u3002 1 Laponite\u7684\u805a\u96c6\u901f\u7387 \u80f6\u4f53\u7c92\u5b50\u7684\u805a\u96c6\uff08coagulation\uff09\u8fc7\u7a0b\u53ef\u5206\u4e3a\u6269\u6563\u63a7\u5236\u578b\u548c\u53cd\u5e94\u63a7\u5236\u578b\u3002\u6269\u6563\u63a7\u5236\u578b\u662f\u7531\u4e8e\u7c92\u5b50\u4e4b\u95f4\u805a\u96c6\u53cd\u5e94\u5341\u5206\u5feb\uff08\u6d3b\u5316\u80fd\u4e3a\u96f6\uff09\uff0c\u56e0\u6b64\u53cd\u5e94\u901f\u7387\u57fa\u672c\u53ea\u53d7\u5236\u4e8e\u78b0\u649e\u673a\u7387\u3002\u6839\u636e\u5e03\u6717\u8fd0\u52a8\u7684\u516c\u5f0f\uff0c\u53ef\u4ee5\u5199\u51fa\u5176\u901f\u7387\u5e38\u6570\u3002\u800c\u53cd\u5e94\u63a7\u5236\u578b\u5219\u662f\u7531\u4e8e\u7c92\u5b50\u95f4\u6210\u529f\u5730\u7ed3\u5408\u9700\u8981\u514b\u670d\u80fd\u5792Umax\u56e0\u800c\u5e76\u975e\u6240\u6709\u78b0\u649e\u4e8b\u4ef6\u90fd\u80fd\u6210\u529f\u53d1\u751f\u805a\u96c6\uff0c\u5176\u901f\u7387\u5e38\u6570\u5c31\u8981\u6bd4\u4ec5\u53d7\u6269\u6563\u63a7\u5236\u7684kD\u5c0f\u3002\u5b9a\u4e49stability ratio\uff0cW = kD \/ kR\uff0c\u4ee5\u8868\u5f81\u53cd\u5e94\u96be\u5ea6\uff08Umax\uff09\u5bf9\u805a\u96c6\u8fc7\u7a0b\u5feb\u6162\u7684\u963b\u788d\u7a0b\u5ea6\uff0c\u5219W\u5e94\u8be5\u8ddfUmax\u6709\u5173\uff08\u4ee5\u4e0a\u53ef\u53c2\u89c1T. Cosgrove\u7b49\u5408\u7f16\u7684\u4e66[1]\uff09\u3002N. Fuch[2]\u5b9a\u4e49\uff0c\u53ef\u7528\u4e8e\u4eceU(h)\u8ba1\u7b97W\uff0c\u4f46U(r)\u7684\u5f62\u5f0f\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u805a\u5408\u7269\u5438\u9644\u6a21\u578b\uff08\u5982Scheutjens\u2013Fleer\u7684\u5e73\u5747\u573a\u7406\u8bba\u8fd8\u662fde Gennes\u7684\u6807\u5ea6\u7406\u8bba\uff09\u4e14\u8868\u8fbe\u5f0f\u590d\u6742\uff08\u56e0\u4e3a\u8fd8\u8981\u52a0\u4e0a\u8303\u5fb7\u534e\u52bf\u548c\u9759\u7535\u52bf\uff09\uff0c\u56e0\u6b64\u5b9e\u9645\u4e0a\u5f80\u5f80\u76f4\u63a5\u91c7\u7528W\u7684\u8fd1\u4f3c\u5f0f\u3002\u4f8b\u5982S. Tawari\u7b49\u548cA. Nelson\u7b49[3, 4]\u91c7\u7528\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u6765\u63cf\u8ff0Laponite\u60ac\u6d6e\u6db2\u7684\u8001\u5316\uff1a \u4e0a\u5f0f\u672c\u6765\u662fPrieve and Ruckenstein[5]\u4e3a\u7403\u5f62\u7c92\u5b50\u5bfc\u51fa\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff0cLaponite\u4f5c\u4e3a\u975e\u7403\u72b6\u7c92\u5b50\uff0c\u7cfb\u65700.25\u5e94\u8be5\u504f\u5927\uff0c\u4f46\u8fd9\u4e00\u7cfb\u6570\u503c\u7684\u53d8\u5316\u5bf9W\u7684\u5927\u5c0f\u5f71\u54cd\u5f88\u5c0f\uff08\u89c1S. Tawari\u7b49\u7684\u8ba8\u8bba[3]\uff09\uff0c\u5012\u4e5f\u53ef\u4ee5\u4e0d\u53bb\u4fee\u6539\u3002\u5982\u679c\u672c\u6587\u4e5f\u91c7\u7528\u6b64\u5f0f\uff0c\u5219\u6709kR ~ W-1 ~ exp(-Umax\/kBT)\u3002 \u6839\u636eSmoluchowski\u805a\u96c6\u7406\u8bba\u7684\u5047\u8bbe\uff0c\u805a\u96c6\u8fc7\u7a0b\u662f\u4e00\u4e2a\u4e8c\u7ea7\u53cd\u5e94\u63a7\u5236\u805a\u96c62A\u2192P\uff0c\u4ea7\u7269\u751f\u6210\u91cfP\u968f\u65f6\u95f4\u7684\u53d8\u5316\u5173\u7cfb\u662f\uff1a \u5176\u4e2d\uff0cA0\u662f\u53cd\u5e94\u7269\u7684\u91cf\uff08\u4f5c\u4e3a\u7c92\u5b50\u805a\u96c6\u4f53\u7cfb\u5c31\u662f\u521d\u59cb\u7c92\u5b50\u6570\uff09\uff0ck\u662f\u53cd\u5e94\u6570\u7387\u5e38\u6570\uff08\u5373\u524d\u6587\u7684kR\uff09\u3002\u5bf9\u4e8e\u672c\u6587\u7684\u4f53\u7cfb\uff0cPEG\u7684\u6dfb\u52a0\u4f7f\u5f97Laponite\u8001\u5316\u7684\u8fc7\u7a0b\u88ab\u63d0\u524d\uff0c\u5c31\u662f\u7531\u4e8e\u805a\u5408\u7269\u7684\u4f4d\u963b\u4f5c\u7528\uff0c\u589e\u5927\u4e86Umax\u3002\u800c\u4e14Umax\u4e0ePEG\u6d53\u5ea6cp\u6709\u5173\uff0c\u56e0\u800c\u6570\u7387\u5e38\u6570k\u4e5f\u4e0ecp\u6709\u5173\u3002\u5982\u679c\u4e0d\u540ccp\u4e0b\u7684\u66f2\u7ebfP(tw, cp)\u5728\u65f6\u95f4\u5c3a\u5ea6\u4e0a\u6709\u53e0\u52a0\u6027\u4e14\u5e73\u79fb\u56e0\u5b50\u4e3aap(cp)\u3001\u53e0\u52a0\u540e\u4e3b\u66f2\u7ebf\u7684\u6a2a\u5750\u6807\u4e3atw\/ap\uff0c\u90a3\u4e48\u5c31\u6709k(cp)\/ap = k0\uff08k0\u4e3a\u53c2\u8003\u66f2\u7ebf\u7684\u901f\u7387\u5e38\u6570\uff09\uff0c\u5373ap ~ k-1 ~ W ~ exp(Umax\/kBT)\u3002\u8fd9\u5c31\u662f\u5e73\u79fb\u56e0\u5b50\u4e0eUmax\u7684\u5173\u7cfb\u3002 Y. Joshi\u66fe\u628aLaponite\u8001\u5316\u53e0\u52a0\u66f2\u7ebf\u7684\u6c34\u5e73\u5e73\u79fb\u56e0\u5b50\u4e0eexp(Umax\/kBT)\u76f8\u8054\u7cfb\uff0c\u4f46\u6ca1\u6709\u4e25\u683c\u89e3\u91ca\uff0c\u53ea\u662f\u4e00\u53e5\u5e26\u8fc7[6]\u3002 \u5269\u4e0b\u7684\u95ee\u9898\uff0c\u5c31\u662fUmax\u4e0ecp\u7684\u5173\u7cfb\u3002 2 Laponite\u7684\u7c92\u5b50\u95f4\u4f5c\u7528\u52bf \u00a0 \u6309\u7167\u6211\u60f3\u8c61\uff0c\u6c42Umax\u7684\u65b9\u6cd5\u5c31\u662f\u53bb\u6c42U(h)\u51fd\u6570\u7684\u6781\u5927\u503c\uff0c\u5148\u6c42\u5bfc\u518d\u89e3\u65b9\u7a0b\u3002\uff08\u4e0d\u77e5\u9053\u6570\u5b66\u4e0a\u662f\u5426\u6709\u5176\u4ed6\u53d6\u5de7\u7684\u65b9\u6cd5\uff09\uff0c\u56e0\u6b64\u8981\u77e5\u9053U(h)\u7684\u5177\u4f53\u5f62\u5f0f\u3002 \u60ac\u6d6e\u5e26\u7535\u7c92\u5b50\u95f4\u7684\u4f5c\u7528\u52bf\u51fd\u6570U(h)\u662f\u6307\u628a\u4e24\u4e2a\u7c92\u5b50\u4ece\u8ddd\u79bb\u65e0\u9650\u8fdc\u79fb\u52a8\u81f3\u8ddd\u79bb\u4e3ah\u6240\u9700\u8981\u514b\u670d\u7684\u80fd\u91cf\u3002\u5b83\u53ef\u4ee5\u770b\u4f5c\u662f\u4e09\u4e2a\u90e8\u5206\u7684\u52a0\u548c\uff1a\u3002\u9759\u7535\u76f8\u4e92\u4f5c\u7528\uff08\u53cc\u7535\u5c42\uff09\u53ef\u91c7\u7528UDL(h) = CDLexp(-\u03bah)\uff0c\u5176\u4e2dCDL\u4e3a\u5e38\u6570\u3002\u8be5\u5f0f\u9002\u7528\u4e8e\u03ba > 3\u7684\u60c5\u51b5\u3002\u8303\u5fb7\u534e\u529b\u53ef\u91c7\u7528UA(h) = -Aa\/12h\uff0c\u5176\u4e2dA\u4e3aHamacker\u5e38\u6570\uff0ca\u4e3a\u6837\u54c1\u7684\u534a\u5f84\uff0c\u8be5\u5f0f\u9002\u7528\u4e8eh <<\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"clip_image002","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/clip_image002_thumb.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":4296,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4296","url_meta":{"origin":2406,"position":5},"title":"\u91cd\u65b0\u8003\u8651Laponite\u7c92\u5b50\u95f4\u4f5c\u7528\u52bf\u80fd","author":"Andrew","date":"2011\u5e7411\u67086\u65e5","format":false,"excerpt":"\u9000\u56de\u7684\u5ba1\u7a3f\u610f\u89c1\u53cd\u6620\u7a3f\u5b50\u7684\u6700\u5927\u95ee\u9898\u5728\u4e8e\u5bf9Laponite\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u7684\u8003\u8651\u4e0d\u5468\u3002\u9700\u8981\u5bf9\u539f\u672c\u7684model\u8fdb\u884c\u6bd4\u8f83\u5927\u7684\u4fee\u6539\u3002 Laponite\u7c92\u5b50\u5f62\u72b6\u4e0e\u5e26\u7535\u7684\u5404\u5411\u5f02\u6027 \u5ba1\u7a3f\u4eba\u53d1\u96be\u7684\u6700\u4e3b\u8981\u4e00\u70b9\u5c31\u662f\u6211\u6ca1\u6709\u8003\u8651Laponite\u7c92\u5b50\u5728\u5f62\u72b6\u4e0a\u548c\u8868\u9762\u5e26\u7535\u5206\u5e03\u4e0a\u7684\u5404\u5411\u5f02\u6027\u3002Laponite\u662f\u7247\u72b6\u7c92\u5b50\uff0c\u4e24\u4e2a\u9762\uff08face\uff09\u5e26\u8d1f\u7535\uff0c\u8fb9\u7f18\uff08edge\uff09\u5e26\u6b63\u7535\u3002\u56e0\u6b64\uff0c\u4e24\u4e2aLaponite\u7c92\u5b50\u7684\u76f8\u4e92\u4f5c\u7528\u5c31\u8981\u5206\u4e3aface-face\u3001face-edge\u548cedge-edge\u6765\u8ba8\u8bba\u3002\u800c\u4e14\uff0c\u8fd9\u4e09\u79cd\u76f8\u4e92\u4f5c\u7528\u53d1\u751f\u7684\u673a\u7387\u5728\u5728\u91cfLaponite\u7c92\u5b50\u7cfb\u7edf\u4e2d\u5982\u4f55\u5206\u5e03\u4e5f\u9700\u8981\u4f30\u8ba1\u3002\u540e\u8005\u6d89\u53ca\u5230\u53d6\u5411\uff0c\u5f53\u521d\u5c31\u4f30\u8ba1\u7cbe\u786e\u8003\u8651\u53d6\u5411\u673a\u7387\u53ef\u80fd\u4f1a\u5f88\u96be\uff0c\u539f\u672c\u5c31\u6253\u7b97\u7cbe\u786e\u6210\u7403\u578b\u7684\u3002\u73b0\u5728\u65e2\u7136\u5ba1\u7a3f\u4eba\u8bf4\u201c\u771f\u7a7a\u7403\u5f62\u9e21\u201d\u4e0d\u9760\u8c31\u4e86\uff0c\u6211\u53c8\u5728\u6709\u9650\u7684\u65f6\u95f4\u5185\u67e5\u9605\u4e86\u4e00\u4e0b\u6587\u732e\uff0c\u8fd8\u662f\u5f88\u96be\u627e\u5230\u6709\u6587\u732e\u76f4\u63a5\u4ece\u7406\u8bba\u4e0a\u8003\u8651Laponite\u7684\u53d6\u5411\u3002 Secor\u548cRadke\u7ed9\u51fa\u4e86Poisson-Boltzmann\u65b9\u7a0b\u5728\u5706\u67f1\u8584\u7247\u72b6\u80f6\u4f53\u7c92\u5b50\uff0c\u8868\u9762\u5e26\u8d1f\u7535\u3001\u8fb9\u7f18\u5e26\u6b63\u7535\u60c5\u51b5\u4e0b\u7684\u89e3\u6790\u89e3\uff0c\u672c\u6765\u5e94\u8be5\u95ee\u9898\u5c31\u7ed3\u4e86\u3002\u4f46\u6839\u636e\u6587\u7ae0\u7684\u6458\u8981\uff08\u5168\u6587\u6211\u4e0b\u4e0d\u4e86\uff09\uff0c\u8ba1\u7b97\u7ed3\u679c\u662f\u9762\u4e0a\u5e26\u7684\u8d1f\u7535\u7535\u52bf\u5206\u5e03\u6ea2\u51fa\u5230\u4e86\u8fb9\u7f18\u4e0a\uff0c\u6240\u4ee5\u5c31\u7b97\u8fb9\u7f18\u4e0a\u5e26\u6709\u6b63\u7535\u8377\uff0c\u4e5f\u662f\u8d1f\u7535\u52bf\uff0c\u5373edge-face\u662f\u540c\u79cd\u7535\u8377\uff0c\u4e0d\u5b58\u5728\u5f15\u529b\u3002\u8fd9\u8ddfLaponite\u7684\u76ee\u524d\u516c\u8ba4\u7684\u7269\u7406\u56fe\u50cf\u4e0d\u7b26\u3002\u4e0d\u8fc7\u5149\u4ece\u6458\u8981\u8fd8\u770b\u4e0d\u51fa\u539f\u6587\u5728\u8ba1\u7b97\u65f6\u8bbe\u5b9a\u7684\u8fb9\u7f18\u6b63\u7535\u8377\u5927\u5c0f\u662f\u591a\u5c11\uff0c\u4e5f\u8bb8\u662f\u53d6\u503c\u592a\u5c0f\u7684\u7f18\u6545\u3002\u9664\u4e86Poisson-Boltzmann\u65b9\u7a0b\u7684\u7cbe\u786e\u89e3\uff0c\u8fd8\u6709\u5404\u79cd\u8fd1\u4f3c\u65b9\u6cd5\u5efa\u7acb\u4e0d\u540c\u53d6\u5411\u65b9\u5f0f\u7684\u4f5c\u7528\u52bf\u80fd\u51fd\u6570\u3002\u4f8b\u5982\uff0cDjikstra\u7b49\u628aLaponite\u7c92\u5b50\u8003\u8651\u6210\u65e0\u9650\u8584\u7684\u5706\u7247\uff0c\u5176\u5e26\u7535\u60c5\u51b5\u8fd1\u4f3c\u4e3a\u7535\u56db\u6781\u77e9\uff08quadrupole\uff09\uff0cKutter\u7b49\u628aLaponite\u7c92\u5b50\u7684\u5e26\u7535\u60c5\u51b5\u8003\u8651\u6210\u82e5\u5e72\u4e2a\u70b9\u7535\u8377\u7684\u5e73\u9762\u9635\u5217\u7684\u603b\u6548\u679c\u3002\u4f46\u65e0\u8bba\u5982\u4f55\u8003\u8651\u52bf\u80fd\u51fd\u6570\uff0c\u90fd\u8981\u518d\u8fdb\u884cMonte Carlo\u6a21\u62df\uff0c\u624d\u5f97\u5230\u53d6\u5411\u76f8\u5173\u51fd\u6570gor(r)\u3002\u6211\u79c1\u4e0b\u7528\u201c\u542c\u5929\u7531\u547d\u201d\u8fd9\u4e2a\u8bcd\u6765\u5f62\u5bb9\u62ff\u8ba1\u7b97\u673a\u6a21\u62df\u6765\u5c1d\u8bd5\u4e8b\u5148\u9884\u6d4b\u4e0d\u6765\u7684\u4e8b\u60c5\uff0c\u56e0\u89c9\u5f97\u8fd9\u4e0d\u4f26\u4e0d\u7c7b\u3002\u672c\u6765\u4f60\u7684\u6a21\u578b\u5c31\u5f85\u5b9e\u9a8c\u9a8c\u8bc1\uff0c\u7ed3\u679c\u4f60\u53c8\u7528\u8fd9\u4e2a\u6a21\u578b\u6765\u505a\u8ba1\u7b97\u673a\u6a21\u62df\uff08\u5373\u5b9e\u9a8c\uff09\u3002 Dur\u00e1n\u7b49\u628aedge\u548cface\u5f53\u6210\u4e24\u76f8\uff0c\u52a0\u4e0a\u6eb6\u5242\u5c31\u4e00\u5171\u4e09\u76f8\u3002\u7136\u540eLaponite\u7c92\u5b50\u95f4\u7684\u53cc\u7535\u5c42\u76f8\u4e92\u4f5c\u7528\u53ef\u901a\u8fc7HHF\u6a21\u578b\u6765\u5206\u522b\u8ba1\u7b97edge-face\u3001face-face\u548cedge-edge\u4e09\u79cd\u60c5\u51b5\u3002\u4f46\u662f\uff0c\u8fd9\u7bc7\u6587\u7ae0\u7684\u903b\u8f91\u662f\u901a\u8fc7\u7535\u6cf3\u6cd5\u5b9e\u6d4b\u6837\u54c1\u7684\u03b6-\u7535\u4f4d\uff0c\u7136\u540e\u6309\u7167\u7c98\u571f\u7684\u7ed3\u6784\u6765\u5047\u8bbe\u6d4b\u5f97\u7684\u03b6-\u7535\u4f4d\u4e2d\u767e\u5206\u51e0\u662fedge\u7684\uff0c\u767e\u5206\u4e4b\u51e0\u662fface\u7684\uff0c\u4ee3\u5165HHF\u6a21\u578b\u5206\u522b\u7b97\u51fa\u4e09\u79cd\u4f5c\u7528\u52bf\u80fd\u3002\u6574\u7bc7\u6587\u7ae0\u7684\u8ba8\u8bba\u4e2d\uff0c\u4e09\u79cd\u4f5c\u7528\u52bf\u80fd\u90fd\u662f\u5206\u5f00\u7684\u8ba8\u8bba\u7684\uff0c\u6ca1\u6709\u7efc\u5408\u8d77\u6765\u8fc7\uff0c\u56e0\u6b64\u4e5f\u7528\u4e0d\u7740\u8003\u8651\u8fd9\u4e09\u79cd\u60c5\u51b5\u8c01\u591a\u8c01\u5c11\u7684\u95ee\u9898\u2014\u2014\u5373Laponite\u53d6\u5411\u5206\u5e03\u7684\u95ee\u9898\u4e86\u3002 \u7531\u4e8e\u771f\u5b9e\u4e16\u754c\uff08\u975e\u8ba1\u7b97\u673a\u6a21\u62df\uff09\u7684\u5b9e\u9a8c\u624b\u6bb5\u5927\u591a\u65e0\u6cd5\u5206\u8fa8Laponite\u7c92\u5b50\u53d6\u5411\u5206\u5e03\u3002\u5e38\u7528\u7684\u52a8\u6001\u5149\u6563\u5c04\u6cd5\u6d4b\u7c92\u5f84\u548c\u7535\u6cf3\u6cd5\u6d4b\u03b6-\u7535\u4f4d\u90fd\u662f\u5047\u8bbe\u7c92\u5b50\u4e3a\u7403\u5f62\u5f97\u5230\u5b9e\u9a8c\u7ed3\u679c\u7684\u3002\u6240\u4ee5\u5c31\u7b97\u4f60\u80fd\u4ece\u7406\u8bba\u4e0a\u7ed9\u51fa\u53d6\u5411\u5206\u5e03\u7684\u5b9a\u91cf\u5173\u7cfb\uff0c\u9664\u8ba1\u7b97\u673a\u6a21\u62df\u4ee5\u5916\u4e5f\u7f3a\u4e4f\u5b9e\u9a8c\u9a8c\u8bc1\u624b\u6bb5\uff0c\u8003\u8651\u4e86\u4e5f\u767d\u8003\u8651\u3002\u56e0\u6b64\u6211\u4e0d\u592a\u7406\u89e3\u5ba1\u7a3f\u4eba\u662f\u5426\u975e\u8981\u6211\u5b9e\u7259\u5b9e\u9f7f\u5730\u8003\u8651face-edge\u76f8\u4e92\u4f5c\u7528\u4e0d\u53ef\u3002\u6211\u770b\u5230University of Washington\u7684J. Berg\u7ec4\u6709\u4e00\u7bc7\u7814\u7a76Laponite\u6d41\u53d8\u5b66\u7684\u6587\u7ae0\u76f4\u63a5\u628a\u7c92\u5b50\u5f53\u7403\u5f62\u8003\u8651\u4e86\uff0c\u4f46\u6709\u4e00\u6bb5\u5173\u4e8eedge\u548cface\u7684\u89e3\u91ca\u6587\u5b57\u5982\u4e0b\uff08\u91cd\u70b9\u662f\u6211\u52a0\u7684\uff09\uff1a The electrical surface potential must now account for the face and edge potential separately. This gives the following estimate [math]\\mathit{\\Phi}_\\textup{e}\\approx 2\\pi\\epsilon\\epsilon_0 a\\psi _\\textup{face}\\psi_\\textup{edge}\\ln\\left[\\frac{1}{1-\\exp\\left(-\\kappa D \\right )} \\right ].[\/math] The Larson anlysis went from this point to replace the surface potential\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/2406","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/comments?post=2406"}],"version-history":[{"count":27,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/2406\/revisions"}],"predecessor-version":[{"id":2504,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/2406\/revisions\/2504"}],"wp:attachment":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/media?parent=2406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/categories?post=2406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/tags?post=2406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}