{"id":9243,"date":"2025-08-02T04:44:41","date_gmt":"2025-08-01T20:44:41","guid":{"rendered":"https:\/\/www.andrewsun.net\/panta_rhei\/?p=9243"},"modified":"2025-08-02T04:55:36","modified_gmt":"2025-08-01T20:55:36","slug":"%e4%b8%ad%e5%9b%bd%e5%92%8c%e8%8b%b1%e5%9b%bd%e7%bb%9f%e8%ae%a1%e5%8a%9b%e5%ad%a6%e5%ae%b6%e5%9c%a8%e9%ab%98%e5%88%86%e5%ad%90%e6%ba%b6%e6%b6%b2%e7%83%ad%e5%8a%9b%e5%ad%a6%e7%9a%84%e8%b4%a1%e7%8c%ae","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9243","title":{"rendered":"\u4e2d\u56fd\u548c\u82f1\u56fd\u7edf\u8ba1\u529b\u5b66\u5bb6\u5728\u9ad8\u5206\u5b50\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u8d21\u732e"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"9243\">\n\n<p>\u6211\u4eec\u90fd\u77e5\u9053Flory&#8211;Huggins\u6eb6\u6db2\u7406\u8bba\u4e2d\u7684\u6df7\u5408\u71b5\uff0c\u5c31\u662f\u628a\u7406\u60f3\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u8868\u8fbe\u5f0f\u4e2d\u7684\u6469\u5c14\u5206\u6570\u6539\u6210\u4e86\u4f53\u79ef\u5206\u6570\u3002\u4ee5\u4e8c\u5143\u6db2\u6001\u6df7\u5408\u7269\u4e3a\u4f8b\uff0c<br \/>$$\\Delta_\\text{mix}G^\\text{id}=-T\\Delta_\\text{mix}S^\\text{id}=RT\\left[n_1\\ln x_1+n_2\\ln x_2\\right]$$<br \/>\u800cFlory&#8211;Huggins\u7406\u8bba\u7ed9\u51fa\u7684\u5c0f\u5206\u5b50\u6eb6\u5242+\u7ebf\u5f62\u9ad8\u805a\u7269\u6eb6\u8d28\u7684\u7ed3\u679c\u662f\uff1a<br \/>$$\\Delta_\\text{mix}S=-R\\left[n_1\\ln\\varphi_1+n_2\\ln\\varphi_2\\right]$$<br \/>\u4ee5\u4e0a\u8ba8\u8bba\u90fd\u5047\u5b9a$\\Delta_\\text{mix}H=0$\uff0c\u6216\u8005\u9650\u4e8e\u683c\u5b50\u6a21\u578b\u6765\u8bf4\u5c31\u662f\u4e0d\u540c\u6784\u5f62\u7684\u5185\u80fd\u76f8\u540c\u3002\u8fd9\u88ab\u79f0\u4e3a\u65e0\u70ed\uff08athermal\uff09\u6eb6\u6db2\uff08\u662f\u56e0\u4e3a\u7113\u5386\u53f2\u4e0a\u88ab\u79f0\u4e3a\u201cheat\u201d\uff0c\u5176\u5b9e\u8fd9\u8ddf\u70ed\u5bb9\u6216\u71b5\u4e0d\u76f4\u63a5\u76f8\u5173\uff0c\u53cd\u800c\u662f\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd\u7684\u4f53\u73b0\uff09\u3002\u5982\u679c\u6309\u7167\u60ef\u4f8b\u7528\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7406\u60f3\u6df7\u5408\u7269\u4f5c\u4e3a\u6807\u51c6\u6001\uff0c\u90a3\u4e48Flory&#8211;Huggins\u7684\u7ed3\u679c\u4f53\u73b0\u7684\u7ed3\u8bba\u5c31\u662f\uff0c\u4ec5\u56e0\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u4e5f\u4f1a\u5236\u9020\u51fa\u975e\u96f6\u7684\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\uff0c\u4e14\u8fd9\u4e2a\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\u662f\u7eaf\u71b5\u53d8\u3002<\/p>\n\n\n\n<p>\u65e9\u671f\u8ba4\u4e3a\uff0c\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u662f\u8981\u901a\u8fc7\u5b83\u4eec\u9020\u6210\u4e86\u76f8\u4e92\u4f5c\u7528\u52bf\u7684\u4e0d\u5bf9\u79f0\uff0c\u5373\u975e\u96f6\u7684\u4ea4\u6362\u80fd$w\\equiv w_{AB}-\\left(1\\middle\/2\\right)\\left(w_{AA}+w_{BB}\\right)$\uff0c\u6bd5\u7adf\u5206\u5b50\u5927\u5c0f\u9996\u5148\u5c31\u5f71\u54cd\u8272\u6563\u529b\u3002\u5230\u4e86\u5927\u69821930\u5e74\u4e2d\u53f6\uff08\u57281936\u5e74\u7684\u6cd5\u62c9\u7b2c\u5b66\u4f1a\u7b2c65\u6b21\u4e00\u822c\u8ba8\u8bba\u4e2d\uff09\uff0c\u5927\u5bb6\u624d\u63a5\u53d7\u4e0d\u540c\u5206\u5b50\u5c3a\u5bf8\u7684<em>\u65e0\u70ed<\/em>\u6df7\u5408\u7269\u6709\u8d85\u989d\u71b5\u3002R. Fowler\u63d0\u51fa\u5927\u4e00\u70b9\u7684\u5206\u5b50\u53ef\u4ee5\u8003\u8651\u5360\u4e24\u4e2a\u683c\u5b50\u3002\u4ed6\u548cG. Rushbrook\u53d1\u8868\u7684\u8fd9\u79cd\u8ba1\u7b97\u7ed3\u679c<span id=\"cite_ITEM-9243-0\" name=\"citation\"><a href=\"#ITEM-9243-0\">[1]<\/a><\/span>\u8bc1\u5b9e\u4e86\u8fd9\u4ef6\u4e8b\u3002\u4ec5\u4ec5\u4f5c\u51fa\u8fd9\u4e00\u5c0f\u6b65\u7684\u63a8\u5e7f\uff0c\u6570\u5b66\u63a8\u5bfc\u7684\u96be\u5ea6\u5c31\u5927\u589e\u3002\u539f\u6587\u53ea\u8ba8\u8bba\u4e86$N_1\\ll N_2$\u6216$N_1\\gg N_2$\u7684\u60c5\u51b5\u3002H. Bethe\u63d0\u51fa\u4e86\u4e00\u79cd\u65b9\u6cd5<span id=\"cite_ITEM-9243-1\" name=\"citation\"><a href=\"#ITEM-9243-1\">[2]<\/a><\/span>\uff0c\u73b0\u5728\u79f0\u4e3aBethe&#8211;Peierls\u8fd1\u4f3c\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u8003\u8651\u4e8c\u4f53\u76f8\u5173\u6027\u4e0b\u7684\u6784\u5f62\u6570\uff0c\u5373\u53ef\u5f97\u5230\u6982\u7387$p_{ij},\\quad i,j=A,B$\u3002\u8fd9\u4e2a\u65b9\u6cd5\u8fc5\u901f\u88ab\u5f20\u5b97\u71e7\u548cA. Miller\u7b49\u7528\u4e8e\u8003\u8651\u5927\u5206\u5b50\u6eb6\u8d28\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4ece\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u4e00\u76f4\u63a8\u5e7f\u5230\u4e00\u822c\u7684$r$\u805a\u4f53<span id=\"cite_ITEM-9243-2\" name=\"citation\"><a href=\"#ITEM-9243-2\">[3]<\/a><\/span><span id=\"cite_ITEM-9243-3\" name=\"citation\"><a href=\"#ITEM-9243-3\">[4]<\/a><\/span><span id=\"cite_ITEM-9243-4\" name=\"citation\"><a href=\"#ITEM-9243-4\">[5]<\/a><\/span><span id=\"cite_ITEM-9243-5\" name=\"citation\"><a href=\"#ITEM-9243-5\">[6]<\/a><\/span>\u3002\u8fd9\u4e24\u4e2a\u4eba\u9760Bethe\u65b9\u6cd5\u5199\u4e0b\u6784\u5f62\u6570\uff0c\u5f97\u5230\u65e0\u70ed\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u53d8\u90e8\u5206\u3002W. Orr\u8fdb\u4e00\u6b65\u628aBethe\u8fd1\u4f3c\u4e0b\u7684\u6df7\u5408\u7113\u4e5f\u5199\u51fa\u6765\u4e86<span id=\"cite_ITEM-9243-6\" name=\"citation\"><a href=\"#ITEM-9243-6\">[7]<\/a><\/span><span id=\"cite_ITEM-9243-7\" name=\"citation\"><a href=\"#ITEM-9243-7\">[8]<\/a><\/span>\u3002E. Guggenheim\u7528\u53e6\u4e00\u79cd\u66f4\u4f18\u96c5\u7684\u65b9\u6cd5\uff0c\u5f97\u51fa\u4e86\u8ddf\u7528Bethe\u65b9\u6cd5\u4e00\u6837\u7684\u7ed3\u679c\uff0c\u5e76\u8bc1\u660e\u4e24\u79cd\u65b9\u6cd5\u662f\u7b49\u4ef7\u7684\u3002\u8fd9\u4e9b\u6765\u81ea\u82f1\u56fd\uff08\u548c\u6211\u56fd\u5f20\u5b97\u71e7\u5728\u82f1\u56fd\u7559\u5b66\u65f6\uff09\u7684\u8d21\u732e\uff0c\u57fa\u672c\u7cfb\u7edf\u6027\u5730\u7ec8\u7ed3\u4e86\u805a\u5408\u7269\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7406\u8bba\u5de5\u4f5c\u3002\u53ef\u4ee5\u53c2\u8003A. Miller\u548cE. Guggenheim\u7684\u4e24\u672c\u4e66\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A. Miller (1948), <em>The Theory of Solutions of High Polymers<\/em>, Clarendon<\/li>\n\n\n\n<li>E. Guggenheim (1952), <em>Mixtures<\/em>, Clarendon<br \/>\u4e5f\u53ef\u4ee5\u53c2\u8003H. Tompa\u7684\u4e66\uff1a<\/li>\n\n\n\n<li>H. Tompa (1956), <em>Polymer Solutions<\/em>, Butterworths<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e2aH. Tompa\u4e5f\u662f\u503c\u5f97\u4e00\u8bf4\u7684\uff0c\u4f46\u6211\u53ef\u80fd\u8981\u5c06\u5728\u53e6\u4e00\u7bc7\u6587\u7ae0\u91cc\u8bb2\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u4eca\u5929\u6240\u719f\u77e5\u7684Flory&#8211;Huggins\u5c5e\u4e8e\u540c\u65f6\u671f\u7f8e\u56fd\u4eba\u7684\u5de5\u4f5c\u3002\u6211\u4e4b\u524d\u7684\u6587\u7ae0\u63d0\u5230\uff0c\u662fM. Huggins\u7a0d\u5fae\u6bd4P. Flory\u65e9\u51e0\u4e2a\u6708\u5f00\u59cb\u63a8\u5bfc\u9ad8\u5206\u5b50\u6eb6\u6db2\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4f3c\u4e4e\u8fd9\u79cd\u540c\u65f6\u6027\u662f\u5de7\u5408\uff0c\u4f46\u5176\u5b9eFlory\u8fd9\u4e2a\u505a\u6cd5\u662f\u53d7\u5fb7\u56fd\u5316\u5b66\u5bb6K. Meyer\u7684\u5efa\u8bae\u505a\u7684\u3002K. Meyer\u548cH. Mark\u5408\u8457\u4e86\u4e16\u754c\u4e0a\u7b2c\u4e00\u672c\u9ad8\u5206\u5b50\u79d1\u5b66\u7684\u6559\u79d1\u4e66\u3002<\/p>\n\n\n\n<p>\u503c\u5f97\u5f3a\u8c03\u7684\u662f\uff0c\u4eca\u5929\u7684Flory&#8211;Huggins\u5f62\u5f0f\uff0c\u662fGuggenheim\u4e00\u822c\u5f62\u5f0f\u4e2d\u914d\u4f4d\u6570$z\\to\\infty$\u7684\u7279\u6b8a\u7ed3\u679c\uff0c\u6240\u4ee5\u8868\u8fbe\u5f0f\u4e2d\u4e0d\u663e\u542b$z$\uff08\u4ea4\u6362\u71b5\u53d8\u90e8\u5206\u4e0d\u542b$z$\uff0c\u7113\u53d8\u5bf9$z$\u7684\u4f9d\u8d56\u6027\u5305\u5728\u201c\u76f8\u4e92\u4f5c\u7528\u53c2\u6570\u201d $\\chi$ \u7684\u5b9a\u4e49\u4e2d\u4e86\uff09\u3002\u54ea\u6015\u662f\u9650\u4e8e\u5bfc\u51faFlory&#8211;Huggins\u7684\u4ea4\u6362\u71b5\u5f62\u5f0f\uff0c\u4e5f\u6709\u4e0d\u540c\u7684\u6570\u683c\u5b50\u65b9\u6cd5\u3002\u4eca\u5929\u8bb8\u591a\u4e2d\u6587\u9ad8\u5206\u5b50\u7269\u7406\u6559\u79d1\u4e66\u4e0a\u7684\u6570\u6cd5\uff0c\u5c31\u8ddfFlory\u5728\u81ea\u5df1\u7684\u4e66\u4e2d\u7684\u6570\u6cd5\u6709\u70b9\u4e0d\u540c\uff0c\u4f46\u90fd\u7528\u4e0d\u540c\u7684\u8fd1\u4f3c\u4e3b\u5f20\u51d1\u51fa\u4e86\u76f8\u540c\u7684\u6700\u540e\u7ed3\u679c\u3002\u5176\u4e2d\u4e00\u79cd\u5199\u6cd5\u9700\u8981\u8bf4\u201c\u5047\u5b9a $z$ \u4e0e $z-1$ \u5dee\u522b\u4e0d\u5927\u201d\u3002\u7136\u800c\u57283\u7ef4\u7a7a\u95f4\u4e2d$z$\u7684\u53d6\u503c\u8303\u56f4\u6700\u9ad8\u662f12\uff0c\u4e00\u822c\u8003\u8651 $z$ \u7b49\u4e8e6\u523010\u3002\u8fd9\u6837\u7684\u53d6\u503c\u600e\u4e48\u53ef\u80fd\u8ba4\u4e3a $z$ \u4e0e $z-1$ \u5dee\u522b\u4e0d\u5927\uff1f\u2014\u2014\u9664\u975e\u53d6\u4e86$z\\to\\infty$ \u6781\u9650\u3002\u6240\u4ee5\uff0c\u5176\u5b9e\u4e00\u4e2a\u4e25\u683c\u7684\u6a21\u578b\u63a8\u5bfc\u7ed3\u679c\u5e94\u8be5\u603b\u662f\u663e\u542b\u914d\u4f4d\u6570\u7684\u3002Flory&#8211;Huggins\u8fd9\u4e2a\u4e0d\u542b\u914d\u4f4d\u6570\u7684\u66f4\u6d41\u884c\u7684\u5f62\u5f0f\u4ec5\u4ec5\u662fGuggenheim\u8868\u8fbe\u5f0f\u7684\u4e00\u4e2a\u7279\u6b8a\u6027\u51b5\u3002\u5f53\u7136\uff0c\u5206\u6790\u8868\u660e\uff0c\u4e0d\u540c\u914d\u4f4d\u6570\u7684\u5dee\u522b\uff0c\u5728 $z=2,3,4$ \u65f6\u5341\u5206\u5de8\u5927\uff0c\u4f46 $z&gt;6$ \u65f6\u5dee\u522b\u6bd4\u8f83\u5c0f\uff0c\u90a3\u4e48Flory&#8211;Huggins\u7684\u5f62\u5f0f\u80dc\u5728\u7b80\u6d01\uff0c\u6240\u4ee5\u8fd9\u4ef6\u4e8b\u4e4b\u540e\u4e5f\u5c31\u6ca1\u4eba\u518d\u8ffd\u7a76\u4e86\u800c\u5df2\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\uff0c\u4e00\u90e8\u5206\u540e\u6765\u7684\u4eba\u4f3c\u4e4e\u8ba4\u4e3a\u914d\u4f4d\u6570\u5728\u7269\u7406\u4e0a\u5c31\u4e0d\u5e94\u8be5\u5f71\u54cd\u6eb6\u6db2\u70ed\u529b\u5b66\u6027\u8d28\u3002\u8fd9\u79cd\u770b\u6cd5\u4e0d\u662f\u6765\u81ea\u7269\u7406\u76f4\u89c9\uff0c\u800c\u4ec5\u4ec5\u662fFlory&#8211;Huggins\u6a21\u578b\u957f\u671f\u6559\u5b66\u8bef\u5bfc\u3002\u5f88\u591a\u8bfe\u5802\u8bb2\u89e3\u751a\u81f3\u6559\u79d1\u4e66\u90fd\u4f1a\u53bb\u5f3a\u8c03\u8fd9\u4e2a\u7ed3\u679c\u4e2d\u4e0d\u542b\u914d\u4f4d\u6570\u8fd9\u4ef6\u4e8b\uff0c\u597d\u50cf\u672c\u8be5\u5982\u6b64\u3002\u6070\u6070\u76f8\u53cd\uff0c\u7269\u7406\u76f4\u89c9\u5e94\u8be5\u4f1a\u544a\u8bc9\u6211\u4eec\uff0c\u914d\u4f4d\u6570\u4e0d\u540c\u5c06\u4e25\u91cd\u5f71\u54cd\u70ed\u529b\u5b66\u6027\u8d28\u3002\u4ece\u6a21\u578b\u7684\u89d2\u5ea6\uff0c\u76f8\u540c\u7684\u6eb6\u5242\uff08\u8d28\uff09\u5206\u5b50\u5c5e\u6027\uff0c\u4ec5\u914d\u4f4d\u6570\u4e0d\u540c\uff0c\u5bf9\u5e94\u4e8e\u4ec0\u4e48\u771f\u5b9e\u7269\u7406\u5462\uff1f\u5b83\u53ef\u80fd\u662f\u5206\u5b50\u7684\u975e\u7403\u5f62\u6216\u8005\u5206\u5b50\u7684\u6c38\u4e45\u6781\u6027\u7b49\u5f71\u54cd\u5806\u780c\u7684\u7269\u7406\u56e0\u7d20\uff0c\u800c\u8fd9\u5f53\u7136\u662f\u91cd\u8981\u7684\u70ed\u529b\u5b66\u6027\u8d28\u5f71\u54cd\u56e0\u7d20\u3002<\/p>\n\n\n\n<p>\u6211\u66fe\u7ecfchair\u4e00\u4e2a\u6d41\u53d8\u5b66\u4f1a\u8bae\u7684section\uff0c\u6709\u4e00\u4e2a\u6f14\u8bb2\u8005\u4ecb\u7ecd\u4e86\u4ed6\u7528\u683c\u5b50\u6a21\u578b\u6765\u8003\u8651\u8fc7\u51b7\u6db2\u4f53\u73bb\u7483\u5316\u8f6c\u53d8\u7684\u70ed\u529b\u5b66\u7406\u8bba\u3002\u4ed6\u76f4\u63a5\u4f7f\u7528\u7684\u5c31\u662fFlory&#8211;Huggins\u5f62\u5f0f\u4f5c\u7406\u8bba\u9884\u6d4b\uff0c\u5f53\u7136\u4e3b\u8981\u7ed3\u679c\u662f\u901a\u8fc7MC\u8ba1\u7b97\u673a\u6a21\u62df\u6765\u7ed9\u51fa\u7684\u3002\u4ecb\u7ecd\u5b8c\u4e4b\u540e\uff0c\u573a\u4e0b\u6ca1\u6709\u4eba\u63d0\u95ee\uff08\u53ef\u80fd\u8bdd\u9898\u592a\u6df1\u4e86\uff09\uff0c\u4e8e\u662f\u6211\u8d1f\u8d23\u63d0\u4e86\u4e2a\u95ee\u9898\uff0c\u5c31\u662f\u914d\u4f4d\u6570\u5728\u8fd9\u91cc\u9762\u8d77\u5230\u4ec0\u4e48\u4f5c\u7528\u3002\u56e0\u4e3a\u6211\u5f53\u65f6\u7684\u7269\u7406\u76f4\u89c9\u544a\u8bc9\u6211\uff0c\u914d\u4f4d\u6570\u5c31\u662f\u5806\u780c\u60c5\u51b5\uff0c\u800c\u8fd9\u5c06\u5728\u73bb\u7483\u5316\u8f6c\u53d8\u4e2d\u4ea7\u751f\u975e\u5e38\u91cd\u8981\u7684\u5f71\u54cd\u3002\u4ed6\u7528\u683c\u5b50\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u505a\uff0c\u53ef\u4ee5\u6362\u4e0d\u540c\u7684\u914d\u4f4d\u6570\u6765\u770b\u3002\u4f46\u662f\u8fd9\u4e2a\u6f14\u8bb2\u8005\u4f3c\u4e4e\u89c9\u5f97\u6211\u7684\u95ee\u9898\u662f\u4e0d\u4e86\u89e3\u57fa\u672c\u5e38\u8bc6\uff0c\u5177\u4f53\u5c31\u662f\u201c\u914d\u4f4d\u6570\u4ec5\u4ec5\u662f\u683c\u5b50\u6a21\u578b\u5f15\u5165\u7684\u6982\u5ff5\uff0c\u7406\u5e94\u6ca1\u6709\u7269\u7406\u6548\u5e94\u201d\u8fd9\u4e2a\u201c\u5e38\u8bc6\u201d\u3002\u5f53\u7136\uff0c\u8fd9\u53ef\u80fd\u662f\u6211\u8fc7\u5ea6\u89e3\u8bfb\uff0c\u5b9e\u9645\u4e0a\u4ed6\u53ea\u4f5c\u4e86\u5f88\u9690\u6666\u7684\u56de\u590d\u3002<\/p>\n\n\n\n<p>\u5f20\u5b97\u71e7\u7684\u5de5\u4f5c\uff0c\u540e\u6765\u88ab\u6768\u632f\u5b81\u548c\u674e\u836b\u8fdc\u7ee7\u7eed<span id=\"cite_ITEM-9243-8\" name=\"citation\"><a href=\"#ITEM-9243-8\">[9]<\/a><\/span>\u3002\u6768\u632f\u5b81\u8fd8\u5728\u8bba\u6587\u7684\u811a\u6ce8\u5f3a\u8c03\u4e86\u738b\u7af9\u6eaa\u7684\u8d21\u732e<span id=\"cite_ITEM-9243-9\" name=\"citation\"><a href=\"#ITEM-9243-9\">[10]<\/a><\/span>\u3002\u8bda\u7136\uff0c\u201c\u6211\u5bf9\u7edf\u8ba1\u7269\u7406\u7684\u5174\u8da3\u5373\u662f\u53d7\u4e86\u7af9\u6eaa\u5e08\u7684\u5f71\u54cd\u3002\u201d\uff08\u89c1\uff1a<a href=\"http:\/\/chris.kias.re.kr\/yang.htm\" target=\"_blank\" rel=\"noreferrer noopener\">\u8fd9\u91cc<\/a>\u548c<a href=\"https:\/\/arxiv.org\/pdf\/1010.1838\" target=\"_blank\" rel=\"noreferrer noopener\">\u8fd9\u91cc<\/a>\uff09\u3002\u53ea\u4e0d\u8fc7\u6768\u548c\u674e\u7684\u5de5\u4f5c\u66f4\u9762\u5411\u56fa\u6eb6\u4f53\uff0c\u800c\u5f20\u5b97\u71e7\u548c\u738b\u7af9\u6eaa\u4f5c\u4e3aFowler\u7684\u5b66\u751f\uff0c\u5219\u8ddfFowler\u505a\u6eb6\u6db2\u7684\u52a8\u673a\u66f4\u63a5\u8fd1\u4e9b\u3002<\/p>\n\n\n\n<p>\u5f20\u5b97\u71e7\u5728\u6587\u9769\u671f\u95f4\u4e0d\u5fcd\u65e0\u5c3d\u7684\u6597\u4e89\u548c\u6298\u78e8\uff0c\u4e8e1969\u5e74\u670d\u5b89\u7720\u836f\u81ea\u6740\uff08\u89c1<a href=\"https:\/\/web.archive.org\/web\/20110831002315\/http:\/\/chinsci.bokee.com\/viewdiary.12874327.html\" target=\"_blank\" rel=\"noreferrer noopener\">\u8fd9\u91cc<\/a>\uff09\u3002<\/p>\n\n\n\n<p><\/p>\n<h2>References<\/h2>\n    <ol>\n    <li><a name='ITEM-9243-0'><\/a>\nR.H. Fowler, and G.S. Rushbrooke, \"An attempt to extend the statistical theory of perfect solutions\", <i>Transactions of the Faraday Society<\/i>, vol. 33, pp. 1272, 1937. <a href=\"http:\/\/dx.doi.org\/10.1039\/TF9373301272\">http:\/\/dx.doi.org\/10.1039\/TF9373301272<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-1'><\/a>\nH.A. Bethe, \"Statistical theory of superlattices\", <i>Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences<\/i>, vol. 150, pp. 552-575, 1935. <a href=\"http:\/\/dx.doi.org\/10.1098\/rspa.1935.0122\">http:\/\/dx.doi.org\/10.1098\/rspa.1935.0122<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-2'><\/a>\nT.S. Chang, \"Statistical theory of the adsorption of double molecules\", <i>Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences<\/i>, vol. 169, pp. 512-531, 1939. <a href=\"http:\/\/dx.doi.org\/10.1098\/rspa.1939.0014\">http:\/\/dx.doi.org\/10.1098\/rspa.1939.0014<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-3'><\/a>\nT.S. Chang, \"The number of configurations in an assembly and cooperative phenomena\", <i>Mathematical Proceedings of the Cambridge Philosophical Society<\/i>, vol. 35, pp. 265-292, 1939. <a href=\"http:\/\/dx.doi.org\/10.1017\/S030500410002096X\">http:\/\/dx.doi.org\/10.1017\/S030500410002096X<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-4'><\/a>\nA.R. Miller, \"The number of configurations of a cooperative assembly\", <i>Mathematical Proceedings of the Cambridge Philosophical Society<\/i>, vol. 38, pp. 109-124, 1942. <a href=\"http:\/\/dx.doi.org\/10.1017\/S030500410002226X\">http:\/\/dx.doi.org\/10.1017\/S030500410002226X<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-5'><\/a>\nA.R. Miller, \"The Vapour-Pressure Equations of Solutions and the Osmotic Pressure of Rubber\", <i>Mathematical Proceedings of the Cambridge Philosophical Society<\/i>, vol. 39, pp. 54-67, 1943. <a href=\"http:\/\/dx.doi.org\/10.1017\/S0305004100017680\">http:\/\/dx.doi.org\/10.1017\/S0305004100017680<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-6'><\/a>\nW.J.C. Orr, \"On the calculation of certain higher-order Bethe approximations\", <i>Transactions of the Faraday Society<\/i>, vol. 40, pp. 306, 1944. <a href=\"http:\/\/dx.doi.org\/10.1039\/TF9444000306\">http:\/\/dx.doi.org\/10.1039\/TF9444000306<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-7'><\/a>\nW.J.C. Orr, \"The free energies of solutions of single and multiple molecules\", <i>Transactions of the Faraday Society<\/i>, vol. 40, pp. 320, 1944. <a href=\"http:\/\/dx.doi.org\/10.1039\/TF9444000320\">http:\/\/dx.doi.org\/10.1039\/TF9444000320<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-8'><\/a>\n. C. N. Yang, . Y. Y. Li, and . , \"GENERAL THEORY OF THE QUASI-GHEMICAL METHOD IN THE STATISTICAL THEORY OF SUPERLATTIGES\", <i>Acta Physica Sinica<\/i>, vol. 7, pp. 59, 1947. <a href=\"http:\/\/dx.doi.org\/10.7498\/aps.7.59\">http:\/\/dx.doi.org\/10.7498\/aps.7.59<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9243-9'><\/a>\nC.N. Yang, \"A Generalization of the Quasi-Chemical Method in the Statistical Theory of Superlattices\", <i>The Journal of Chemical Physics<\/i>, vol. 13, pp. 66-76, 1945. <a href=\"http:\/\/dx.doi.org\/10.1063\/1.1724001\">http:\/\/dx.doi.org\/10.1063\/1.1724001<\/a>\n\n\n<\/li>\n<\/ol>\n\n<\/div> <!-- kcite-section 9243 -->","protected":false},"excerpt":{"rendered":"<p>\u6211\u4eec\u90fd\u77e5\u9053Flory&#8211;Huggins\u6eb6\u6db2\u7406\u8bba\u4e2d\u7684\u6df7\u5408\u71b5\uff0c\u5c31\u662f\u628a\u7406\u60f3\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u8868\u8fbe\u5f0f\u4e2d\u7684\u6469\u5c14\u5206\u6570\u6539\u6210\u4e86\u4f53\u79ef\u5206\u6570\u3002\u4ee5\u4e8c\u5143\u6db2\u6001\u6df7\u5408\u7269\u4e3a\u4f8b\uff0c$$\\Delta_\\text{mix}G^\\text{id}=-T\\Delta_\\text{mix}S^\\text{id}=RT\\left[n_1\\ln x_1+n_2\\ln x_2\\right]$$\u800cFlory&#8211;Huggins\u7406\u8bba\u7ed9\u51fa\u7684\u5c0f\u5206\u5b50\u6eb6\u5242+\u7ebf\u5f62\u9ad8\u805a\u7269\u6eb6\u8d28\u7684\u7ed3\u679c\u662f\uff1a$$\\Delta_\\text{mix}S=-R\\left[n_1\\ln\\varphi_1+n_2\\ln\\varphi_2\\right]$$\u4ee5\u4e0a\u8ba8\u8bba\u90fd\u5047\u5b9a$\\Delta_\\text{mix}H=0$\uff0c\u6216\u8005\u9650\u4e8e\u683c\u5b50\u6a21\u578b\u6765\u8bf4\u5c31\u662f\u4e0d\u540c\u6784\u5f62\u7684\u5185\u80fd\u76f8\u540c\u3002\u8fd9\u88ab\u79f0\u4e3a\u65e0\u70ed\uff08athermal\uff09\u6eb6\u6db2\uff08\u662f\u56e0\u4e3a\u7113\u5386\u53f2\u4e0a\u88ab\u79f0\u4e3a\u201cheat\u201d\uff0c\u5176\u5b9e\u8fd9\u8ddf\u70ed\u5bb9\u6216\u71b5\u4e0d\u76f4\u63a5\u76f8\u5173\uff0c\u53cd\u800c\u662f\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd\u7684\u4f53\u73b0\uff09\u3002\u5982\u679c\u6309\u7167\u60ef\u4f8b\u7528\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7406\u60f3\u6df7\u5408\u7269\u4f5c\u4e3a\u6807\u51c6\u6001\uff0c\u90a3\u4e48Flory&#8211;Huggins\u7684\u7ed3\u679c\u4f53\u73b0\u7684\u7ed3\u8bba\u5c31\u662f\uff0c\u4ec5\u56e0\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u4e5f\u4f1a\u5236\u9020\u51fa\u975e\u96f6\u7684\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\uff0c\u4e14\u8fd9\u4e2a\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\u662f\u7eaf\u71b5\u53d8\u3002 \u65e9\u671f\u8ba4\u4e3a\uff0c\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u662f\u8981\u901a\u8fc7\u5b83\u4eec\u9020\u6210\u4e86\u76f8\u4e92\u4f5c\u7528\u52bf\u7684\u4e0d\u5bf9\u79f0\uff0c\u5373\u975e\u96f6\u7684\u4ea4\u6362\u80fd$w\\equiv w_{AB}-\\left(1\\middle\/2\\right)\\left(w_{AA}+w_{BB}\\right)$\uff0c\u6bd5\u7adf\u5206\u5b50\u5927\u5c0f\u9996\u5148\u5c31\u5f71\u54cd\u8272\u6563\u529b\u3002\u5230\u4e86\u5927\u69821930\u5e74\u4e2d\u53f6\uff08\u57281936\u5e74\u7684\u6cd5\u62c9\u7b2c\u5b66\u4f1a\u7b2c65\u6b21\u4e00\u822c\u8ba8\u8bba\u4e2d\uff09\uff0c\u5927\u5bb6\u624d\u63a5\u53d7\u4e0d\u540c\u5206\u5b50\u5c3a\u5bf8\u7684\u65e0\u70ed\u6df7\u5408\u7269\u6709\u8d85\u989d\u71b5\u3002R. Fowler\u63d0\u51fa\u5927\u4e00\u70b9\u7684\u5206\u5b50\u53ef\u4ee5\u8003\u8651\u5360\u4e24\u4e2a\u683c\u5b50\u3002\u4ed6\u548cG. Rushbrook\u53d1\u8868\u7684\u8fd9\u79cd\u8ba1\u7b97\u7ed3\u679c\u8bc1\u5b9e\u4e86\u8fd9\u4ef6\u4e8b\u3002\u4ec5\u4ec5\u4f5c\u51fa\u8fd9\u4e00\u5c0f\u6b65\u7684\u63a8\u5e7f\uff0c\u6570\u5b66\u63a8\u5bfc\u7684\u96be\u5ea6\u5c31\u5927\u589e\u3002\u539f\u6587\u53ea\u8ba8\u8bba\u4e86$N_1\\ll N_2$\u6216$N_1\\gg N_2$\u7684\u60c5\u51b5\u3002H. Bethe\u63d0\u51fa\u4e86\u4e00\u79cd\u65b9\u6cd5\uff0c\u73b0\u5728\u79f0\u4e3aBethe&#8211;Peierls\u8fd1\u4f3c\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u8003\u8651\u4e8c\u4f53\u76f8\u5173\u6027\u4e0b\u7684\u6784\u5f62\u6570\uff0c\u5373\u53ef\u5f97\u5230\u6982\u7387$p_{ij},\\quad i,j=A,B$\u3002\u8fd9\u4e2a\u65b9\u6cd5\u8fc5\u901f\u88ab\u5f20\u5b97\u71e7\u548cA. Miller\u7b49\u7528\u4e8e\u8003\u8651\u5927\u5206\u5b50\u6eb6\u8d28\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4ece\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u4e00\u76f4\u63a8\u5e7f\u5230\u4e00\u822c\u7684$r$\u805a\u4f53\u3002\u8fd9\u4e24\u4e2a\u4eba\u9760Bethe\u65b9\u6cd5\u5199\u4e0b\u6784\u5f62\u6570\uff0c\u5f97\u5230\u65e0\u70ed\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u53d8\u90e8\u5206\u3002W. Orr\u8fdb\u4e00\u6b65\u628aBethe\u8fd1\u4f3c\u4e0b\u7684\u6df7\u5408\u7113\u4e5f\u5199\u51fa\u6765\u4e86\u3002E. Guggenheim\u7528\u53e6\u4e00\u79cd\u66f4\u4f18\u96c5\u7684\u65b9\u6cd5\uff0c\u5f97\u51fa\u4e86\u8ddf\u7528Bethe\u65b9\u6cd5\u4e00\u6837\u7684\u7ed3\u679c\uff0c\u5e76\u8bc1\u660e\u4e24\u79cd\u65b9\u6cd5\u662f\u7b49\u4ef7\u7684\u3002\u8fd9\u4e9b\u6765\u81ea\u82f1\u56fd\uff08\u548c\u6211\u56fd\u5f20\u5b97\u71e7\u5728\u82f1\u56fd\u7559\u5b66\u65f6\uff09\u7684\u8d21\u732e\uff0c\u57fa\u672c\u7cfb\u7edf\u6027\u5730\u7ec8\u7ed3\u4e86\u805a\u5408\u7269\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7406\u8bba\u5de5\u4f5c\u3002\u53ef\u4ee5\u53c2\u8003A. Miller\u548cE. Guggenheim\u7684\u4e24\u672c\u4e66\uff1a \u8fd9\u4e2aH. Tompa\u4e5f\u662f\u503c\u5f97\u4e00\u8bf4\u7684\uff0c\u4f46\u6211\u53ef\u80fd\u8981\u5c06\u5728\u53e6\u4e00\u7bc7\u6587\u7ae0\u91cc\u8bb2\u3002 \u6211\u4eec\u4eca\u5929\u6240\u719f\u77e5\u7684Flory&#8211;Huggins\u5c5e\u4e8e\u540c\u65f6\u671f\u7f8e\u56fd\u4eba\u7684\u5de5\u4f5c\u3002\u6211\u4e4b\u524d\u7684\u6587\u7ae0\u63d0\u5230\uff0c\u662fM. Huggins\u7a0d\u5fae\u6bd4P. Flory\u65e9\u51e0\u4e2a\u6708\u5f00\u59cb\u63a8\u5bfc\u9ad8\u5206\u5b50\u6eb6\u6db2\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4f3c\u4e4e\u8fd9\u79cd\u540c\u65f6\u6027\u662f\u5de7\u5408\uff0c\u4f46\u5176\u5b9eFlory\u8fd9\u4e2a\u505a\u6cd5\u662f\u53d7\u5fb7\u56fd\u5316\u5b66\u5bb6K. Meyer\u7684\u5efa\u8bae\u505a\u7684\u3002K. Meyer\u548cH. Mark\u5408\u8457\u4e86\u4e16\u754c\u4e0a\u7b2c\u4e00\u672c\u9ad8\u5206\u5b50\u79d1\u5b66\u7684\u6559\u79d1\u4e66\u3002 \u503c\u5f97\u5f3a\u8c03\u7684\u662f\uff0c\u4eca\u5929\u7684Flory&#8211;Huggins\u5f62\u5f0f\uff0c\u662fGuggenheim\u4e00\u822c\u5f62\u5f0f\u4e2d\u914d\u4f4d\u6570$z\\to\\infty$\u7684\u7279\u6b8a\u7ed3\u679c\uff0c\u6240\u4ee5\u8868\u8fbe\u5f0f\u4e2d\u4e0d\u663e\u542b$z$\uff08\u4ea4\u6362\u71b5\u53d8\u90e8\u5206\u4e0d\u542b$z$\uff0c\u7113\u53d8\u5bf9$z$\u7684\u4f9d\u8d56\u6027\u5305\u5728\u201c\u76f8\u4e92\u4f5c\u7528\u53c2\u6570\u201d $\\chi$ 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\u6781\u9650\u3002\u6240\u4ee5\uff0c\u5176\u5b9e\u4e00\u4e2a\u4e25\u683c\u7684\u6a21\u578b\u63a8\u5bfc\u7ed3\u679c\u5e94\u8be5\u603b\u662f\u663e\u542b\u914d\u4f4d\u6570\u7684\u3002Flory&#8211;Huggins\u8fd9\u4e2a\u4e0d\u542b\u914d\u4f4d\u6570\u7684\u66f4\u6d41\u884c\u7684\u5f62\u5f0f\u4ec5\u4ec5\u662fGuggenheim\u8868\u8fbe\u5f0f\u7684\u4e00\u4e2a\u7279\u6b8a\u6027\u51b5\u3002\u5f53\u7136\uff0c\u5206\u6790\u8868\u660e\uff0c\u4e0d\u540c\u914d\u4f4d\u6570\u7684\u5dee\u522b\uff0c\u5728 $z=2,3,4$ \u65f6\u5341\u5206\u5de8\u5927\uff0c\u4f46 $z&gt;6$ \u65f6\u5dee\u522b\u6bd4\u8f83\u5c0f\uff0c\u90a3\u4e48Flory&#8211;Huggins\u7684\u5f62\u5f0f\u80dc\u5728\u7b80\u6d01\uff0c\u6240\u4ee5\u8fd9\u4ef6\u4e8b\u4e4b\u540e\u4e5f\u5c31\u6ca1\u4eba\u518d\u8ffd\u7a76\u4e86\u800c\u5df2\u3002 \u4f46\u662f\uff0c\u4e00\u90e8\u5206\u540e\u6765\u7684\u4eba\u4f3c\u4e4e\u8ba4\u4e3a\u914d\u4f4d\u6570\u5728\u7269\u7406\u4e0a\u5c31\u4e0d\u5e94\u8be5\u5f71\u54cd\u6eb6\u6db2\u70ed\u529b\u5b66\u6027\u8d28\u3002\u8fd9\u79cd\u770b\u6cd5\u4e0d\u662f\u6765\u81ea\u7269\u7406\u76f4\u89c9\uff0c\u800c\u4ec5\u4ec5\u662fFlory&#8211;Huggins\u6a21\u578b\u957f\u671f\u6559\u5b66\u8bef\u5bfc\u3002\u5f88\u591a\u8bfe\u5802\u8bb2\u89e3\u751a\u81f3\u6559\u79d1\u4e66\u90fd\u4f1a\u53bb\u5f3a\u8c03\u8fd9\u4e2a\u7ed3\u679c\u4e2d\u4e0d\u542b\u914d\u4f4d\u6570\u8fd9\u4ef6\u4e8b\uff0c\u597d\u50cf\u672c\u8be5\u5982\u6b64\u3002\u6070\u6070\u76f8\u53cd\uff0c\u7269\u7406\u76f4\u89c9\u5e94\u8be5\u4f1a\u544a\u8bc9\u6211\u4eec\uff0c\u914d\u4f4d\u6570\u4e0d\u540c\u5c06\u4e25\u91cd\u5f71\u54cd\u70ed\u529b\u5b66\u6027\u8d28\u3002\u4ece\u6a21\u578b\u7684\u89d2\u5ea6\uff0c\u76f8\u540c\u7684\u6eb6\u5242\uff08\u8d28\uff09\u5206\u5b50\u5c5e\u6027\uff0c\u4ec5\u914d\u4f4d\u6570\u4e0d\u540c\uff0c\u5bf9\u5e94\u4e8e\u4ec0\u4e48\u771f\u5b9e\u7269\u7406\u5462\uff1f\u5b83\u53ef\u80fd\u662f\u5206\u5b50\u7684\u975e\u7403\u5f62\u6216\u8005\u5206\u5b50\u7684\u6c38\u4e45\u6781\u6027\u7b49\u5f71\u54cd\u5806\u780c\u7684\u7269\u7406\u56e0\u7d20\uff0c\u800c\u8fd9\u5f53\u7136\u662f\u91cd\u8981\u7684\u70ed\u529b\u5b66\u6027\u8d28\u5f71\u54cd\u56e0\u7d20\u3002 \u6211\u66fe\u7ecfchair\u4e00\u4e2a\u6d41\u53d8\u5b66\u4f1a\u8bae\u7684section\uff0c\u6709\u4e00\u4e2a\u6f14\u8bb2\u8005\u4ecb\u7ecd\u4e86\u4ed6\u7528\u683c\u5b50\u6a21\u578b\u6765\u8003\u8651\u8fc7\u51b7\u6db2\u4f53\u73bb\u7483\u5316\u8f6c\u53d8\u7684\u70ed\u529b\u5b66\u7406\u8bba\u3002\u4ed6\u76f4\u63a5\u4f7f\u7528\u7684\u5c31\u662fFlory&#8211;Huggins\u5f62\u5f0f\u4f5c\u7406\u8bba\u9884\u6d4b\uff0c\u5f53\u7136\u4e3b\u8981\u7ed3\u679c\u662f\u901a\u8fc7MC\u8ba1\u7b97\u673a\u6a21\u62df\u6765\u7ed9\u51fa\u7684\u3002\u4ecb\u7ecd\u5b8c\u4e4b\u540e\uff0c\u573a\u4e0b\u6ca1\u6709\u4eba\u63d0\u95ee\uff08\u53ef\u80fd\u8bdd\u9898\u592a\u6df1\u4e86\uff09\uff0c\u4e8e\u662f\u6211\u8d1f\u8d23\u63d0\u4e86\u4e2a\u95ee\u9898\uff0c\u5c31\u662f\u914d\u4f4d\u6570\u5728\u8fd9\u91cc\u9762\u8d77\u5230\u4ec0\u4e48\u4f5c\u7528\u3002\u56e0\u4e3a\u6211\u5f53\u65f6\u7684\u7269\u7406\u76f4\u89c9\u544a\u8bc9\u6211\uff0c\u914d\u4f4d\u6570\u5c31\u662f\u5806\u780c\u60c5\u51b5\uff0c\u800c\u8fd9\u5c06\u5728\u73bb\u7483\u5316\u8f6c\u53d8\u4e2d\u4ea7\u751f\u975e\u5e38\u91cd\u8981\u7684\u5f71\u54cd\u3002\u4ed6\u7528\u683c\u5b50\u8499\u7279\u5361\u6d1b\u65b9\u6cd5\u505a\uff0c\u53ef\u4ee5\u6362\u4e0d\u540c\u7684\u914d\u4f4d\u6570\u6765\u770b\u3002\u4f46\u662f\u8fd9\u4e2a\u6f14\u8bb2\u8005\u4f3c\u4e4e\u89c9\u5f97\u6211\u7684\u95ee\u9898\u662f\u4e0d\u4e86\u89e3\u57fa\u672c\u5e38\u8bc6\uff0c\u5177\u4f53\u5c31\u662f\u201c\u914d\u4f4d\u6570\u4ec5\u4ec5\u662f\u683c\u5b50\u6a21\u578b\u5f15\u5165\u7684\u6982\u5ff5\uff0c\u7406\u5e94\u6ca1\u6709\u7269\u7406\u6548\u5e94\u201d\u8fd9\u4e2a\u201c\u5e38\u8bc6\u201d\u3002\u5f53\u7136\uff0c\u8fd9\u53ef\u80fd\u662f\u6211\u8fc7\u5ea6\u89e3\u8bfb\uff0c\u5b9e\u9645\u4e0a\u4ed6\u53ea\u4f5c\u4e86\u5f88\u9690\u6666\u7684\u56de\u590d\u3002 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Which would you like sir?Me: I'd like a cup of ordinary milk please.Server: We don't have that flavor, we only have chocolate etc.Me: No, I'd like a cup of the white stuff that\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":9202,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9202","url_meta":{"origin":9243,"position":1},"title":"\u4f20\u7edf\u6559\u5b66\u5185\u5bb9\u6570\u5b66\u8bed\u8a00\u7684\u8fd1\u4e16\u5316","author":"Andrew","date":"2025\u5e747\u67085\u65e5","format":false,"excerpt":"[latexpage] \u5f88\u591a\u7ecf\u5178\u7269\u7406\u8303\u7574\u7684\u5c0f\u9898\uff0c\u53ef\u80fd19\u4e16\u7eaa\u672b\u7684\u4eba\u52c9\u5f3a\u61c2\u505a\uff0c20\u4e16\u7eaa\u521d\u6216\u8005\u4e2d\u53f6\u7684\u4eba\u4e5f\u61c2\u505a\uff0c\u5f88\u96be\u8bf4\u9700\u8981\u7528\u5230\u4ec0\u4e48\u8fd1\u4e16\u7269\u7406\u5b66\u6210\u679c\uff0c\u4f46\u662f\u4eca\u5929\u7684\u4eba\u505a\u8fd9\u4e9b\u9898\u76ee\u6240\u4f7f\u7528\u7684\u6570\u5b66\u8bed\u8a00\u7167\u6837\u662f\u5341\u5206\u8fd1\u4e16\u5316\u7684\u3002\u8fd9\u4e5f\u8bb8\u662f\u7406\u8bba\u7269\u7406\u7684\u975e\u7ecf\u5178\u90e8\u5206\u5728\u4e8c\u5341\u4e16\u7eaa\u78b0\u5230\u7684\u96be\u9898\u6240\u50ac\u751f\u7684\u6570\u5b66\u8bed\u8a00\u9769\u65b0\u7167\u8fdb\u4e86\u7ecf\u5178\u7269\u7406\u9886\u57df\u7684\u4e00\u79cd\u6548\u5e94\u3002\u7ecf\u5178\u8303\u56f4\u7531\u4e8e\u6570\u5b66\u8bed\u8a00\u548c\u601d\u60f3\u7684\u8fd1\u4e16\u5316\uff0c\u5728\u4e8c\u5341\u4e16\u7eaa\u4e5f\u8bde\u751f\u51fa\u5f88\u591a\u65b0\u7269\u7406\uff0c\u6240\u4ee5\u4e5f\u4e0d\u80fd\u8bf4\u8fd9\u662f\u201c\u6740\u9e21\u7528\u725b\u5200\u201d\uff0c\u4f46\u5f53\u7136\u4e5f\u514d\u4e0d\u4e86\u5f88\u591a\u6ca1\u7ecf\u8fc7\u201c\u5965\u5361\u59c6\u5243\u5200\u201d\u4fee\u526a\u7684\u8fb9\u8fb9\u89d2\u89d2\u3002\u5145\u65a5\u4e8e\u5927\u91cf\u4ee4\u4eba\u6478\u4e0d\u7740\u5934\u8111\u7684\u201c\u9ad8\u89c2\u70b9\u672c\u79d1\u8bb2\u4e49\u201d\u4e2d\u3002 \u7ecf\u5178\u7269\u7406\u77e5\u8bc6\u5f88\u65e9\u5c31\u5df2\u7ecf\u662f\u5927\u5b66\u672c\u79d1\u6559\u5b66\u7684\u5e38\u9a7b\u5185\u5bb9\u3002\u53ea\u4e0d\u8fc7\uff0c\u5c31\u7b97\u8fd9\u4e9b\u5185\u5bb9\u7684\u6570\u5b66\u8bed\u8a00\u6216\u4f53\u7cfb\u5f62\u5f0f\u5728\u4e8c\u5341\u4e16\u7eaa\u5df2\u7ecf\u201c\u8fd1\u4e16\u5316\u201d\u4e86\u4e0d\u6b62\u4e00\u8f6e\u4e86\uff0c\u4f46\u672c\u79d1\u6559\u5b66\u6240\u91c7\u53d6\u7684\u6570\u5b66\u8bed\u8a00\u548c\u4f53\u7cfb\u5f88\u53ef\u80fd\u4ecd\u7136\u662f19\u4e16\u7eaa\u7684\u3002\u5728\u4e2d\u56fd\u7684\u666e\u901a\u9ad8\u6821\u5c24\u4e3a\u5982\u6b64\u3002\u4f46\u51e1\u6211\u4eec\u542c\u8bf4\uff0c\u54ea\u6240\u5927\u5b66\u54ea\u4e2a\u7cfb\u7684\u54ea\u95e8\u8bfe\u8bb2\u4e49\uff0c\u80c6\u6562\u4ece\u67d0\u79cd\u8fd1\u4e16\u6570\u5b66\u7684\u8f83\u9ad8\u89c2\u70b9\u53bb\u8bb2\u67d0\u95e8\u7ecf\u5178\u8bfe\uff0c\u90fd\u4f1a\u5f15\u8d77\u540c\u884c\u4eec\u201c\u5f88update\u3001\u5f88\u8d76\u5f97\u4e0a\u6f6e\u6d41\u3001\u5f88\u4e0d\u8fc7\u65f6\u201d\u7684\u8bc4\u4ef7\uff0c\u540c\u65f6\u5f15\u8d77\u5b66\u751f\u201c\u5f88\u5730\u72f1\u201d\u7684\u8bc4\u4ef7\u3002\u56e0\u4e3a\u672c\u79d1\u666e\u901a\u6570\u5b66\u6559\u5b66\u672c\u8eab\u8fdf\u8fdf\u6ca1\u6709\u5b8c\u6210\u8fd1\u4e16\u5316\u9769\u547d\u3002\u800c\u4e14\u8d8a\u662f\u8fdb\u5165\u5230\u4e8c\u5341\u4e00\u4e16\u7eaa\uff0c\u8d8a\u770b\u4e0d\u5230\u8fd9\u6837\u7684\u53ef\u80fd\u6027\u3002\u5b66\u751f\u5728\u6570\u5b66\u8bfe\u5b66\u7684\u4ecd\u662f19\u4e16\u7eaa\u7684\u4f53\u7cfb\uff0c\u56e0\u6b64\u4e5f\u53ea\u80fd\u6559\u7528\u8fd9\u4e2a\u6570\u5b66\u8bed\u8a00\u5199\u5c31\u7684\u7269\u7406\u7248\u672c\u3002\u6240\u6709\u5b66\u751f\u90fd\u514d\u4e0d\u4e86\u8981\u5728\u7814\u7a76\u751f\u9636\u6bb5\u91cd\u65b0\u4f5c\u8fd1\u4e16\u5316\u5b66\u4e60\u3002\u8fd9\u4e5f\u4f7f\u5f97\u4e00\u4e9b\u8fd1\u4e16\u7269\u7406\u6210\u679c\uff0c\u8fdf\u8fdf\u65e0\u6cd5\u5199\u8fdb\u672c\u79d1\u6559\u4ea7\u4e66\u5f53\u4e2d\uff0c\u56e0\u4e3a\u5b83\u4eec\u4ece\u4e00\u5f00\u59cb\u5c31\u7528\u8fd1\u4e16\u6570\u5b66\u8bed\u8a00\u6765write down\u7684\u3002 P. J. 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Flory\u81ea\u8ff0\u5bf9M. Huggins\u5de5\u4f5c\u7684\u9996\u6b21\u5173\u6ce8","author":"Andrew","date":"2025\u5e747\u670830\u65e5","format":"aside","excerpt":"\u805a\u5408\u7269\u6eb6\u6db2\u7684Flory--Huggins\u7406\u8bba\u662f\u9ad8\u5206\u5b50\u7269\u7406\u7ecf\u5178\u7406\u8bba\u4f53\u7cfb\u4e2d\u7684\u57fa\u77f3\u3002\u5b83\u54ea\u6015\u5341\u5206\u4e0d\u51c6\u786e\uff0c\u4e5f\u88ab\u5f53\u4f5c\u201c\u6807\u51c6\u6a21\u578b\u201d\uff0c\u4f5c\u4e3a\u66f4\u771f\u5b9e\u7406\u8bba\u7684\u53c2\u7167\u3002\u4e4b\u6240\u4ee5\u4f7f\u7528\u8fd9\u4e24\u4e2a\u540d\u5b57\uff0c\u662f\u56e0\u4e3a\u8fd9\u4e24\u4e2a\u4eba\u51e0\u4e4e\u540c\u65f6\u505a\u4e86\u540c\u6837\u7684\u5de5\u4f5c\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u662fMaurice L. Huggins\u5148\u505a\u7684\u3002\u4ece\u53d1\u8868\u7684\u65f6\u95f4\u6765\u770b\uff0cHuggins\u53d1\u8868\u4e8e1941\u5e745\u6708\uff0cFlory\u53d1\u8868\u4e8e\u540c\u5e748\u6708\uff0c\u5e76\u4e14\u5df2\u7ecf\u5f15\u7528\u4e86Huggins\u7684\u5de5\u4f5c\u4e86\u3002\u5b9e\u9645\u4e0a\u8fd9\u4e24\u7bc7\u8bba\u6587\u90fd\u63d0\u5230\u4e86\uff0c\u5728\u540c\u5e74\u76846\u6708\u4efd\u7684\u4e00\u4e2a\u4f1a\u8bae\u2014\u2014Wilder D. 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\u6eb6\u6db2\u7684\u7ed3\u679c\u5dee\u5f88\u8fdc\u3002 \u8fd9\u7c7b\u73b0\u8c61\u88ab\u79f0\u4e3a\u201c\u51dd\u805a\u76f8\u6548\u5e94\u201d\uff08condensed phase effect\uff09\uff1a\u94fe\u95f4\u76f8\u4e92\u4f5c\u7528\u4f1a\u8ba9\u7194\u4f53\u4e2d\u7684\u94fe\u6784\u8c61\u52bf\u80fd\u5206\u5e03\u4e0d\u540c\u4e8e\u201c\u5b64\u7acb\u5355\u94fe\u201d\u7684\u5206\u5e03\u3002 \u4e5f\u6b63\u56e0\u5982\u6b64\uff0c\u628a\u5355\u94fe\u7406\u8bba\u76f4\u63a5\u642c\u5230\u591a\u94fe\u7194\u4f53\u4e0a\uff0c\u6709\u65f6\u53ea\u80fd\u7b97\u662f\u4e00\u79cd phantom chain \/ polymer gas \u7684\u8fd1\u4f3c\u3002 Flory\u5728\u65af\u5766\u798f\u4e4b\u540e\u66f4\u96c6\u4e2d\u5730\u505a\u94fe\u6784\u8c61\u7edf\u8ba1\u3002\u4ed6\u5927\u91cf\u505a RIS \u8ba1\u7b97\u5927\u6982\u4e3b\u8981\u57281970\u5e74\u4e4b\u524d\u3002\u4ed6\u7684\u91cd\u8981\u8457\u4f5c\u300aStatistical Mechanics of Chain Molecules\u300b\u57281969\u5e74\u51fa\u7248\uff0c\u8fd9\u672c\u4e66\u91cc\u5f88\u591a\u63a8\u5bfc\u4e0e\u7ed3\u679c\u5e26\u6709\u201c\u624b\u7b97\u65f6\u4ee3\u201d\u7684\u75d5\u8ff9\uff0c\u56e0\u6b64\u5bf9\u66f4\u9ad8\u9636\u76f8\u5173\u7684\u5904\u7406\u4f1a\u53d7\u5230\u9650\u5236\uff1b\u540e\u6765\u5927\u5bb6\u8f6c\u5411\u7535\u5b50\u8ba1\u7b97\uff0c\u5f88\u591a\u52a8\u529b\u6765\u81ea\u4e8e\u60f3\u628a\u9ad8\u9636\u76f8\u5173\u7cfb\u7edf\u5316\u7b97\u51fa\u6765\u3002\u572820\u4e16\u7eaa60\u5e74\u4ee3\u672b\u81f370\u5e74\u4ee3\u521d\uff0c\u4ed6\u5229\u7528\u65af\u5766\u798f\u5927\u5b66\u7684IBM\u5927\u578b\u8ba1\u7b97\u673a\u4e2d\u5fc3\uff08\u8be5\u4e2d\u5fc3\u56e0\u7f8e\u56fd\u767b\u6708\u8ba1\u5212\u7684\u9700\u6c42\u800c\u5174\u8d77\u6c11\u7528\uff09\uff0c\u6210\u4e3a\u9996\u6279\u5c06\u7535\u5b50\u8ba1\u7b97\u673a\u7528\u4e8e\u79d1\u5b66\u7814\u7a76\u7684\u7814\u7a76\u8005\u4e4b\u4e00\u3002RIS\u8ba1\u7b97\u9700\u8981\u5173\u4e8e\u4e0d\u540c\u6784\u5f62\u4e0b\u4fa7\u57fa-\u4fa7\u57fa\u76f8\u4e92\u4f5c\u7528\u52bf\u7684\u8f93\u5165\uff0c\u624b\u7b97\u7684\u8bdd\uff0c\u53ea\u80fd\u628a\u6cbf\u94fe\u592a\u8fdc\u7684\u76f8\u4e92\u4f5c\u7528\u5ffd\u7565\u6389\uff0c\u5927\u6982\u53ea\u6709\u4e8c\u9636\u76f8\u5173\u7684\u7ed3\u679c\uff1b\u4f7f\u7528\u8ba1\u7b97\u673a\u5c31\u662f\u4e3a\u4e86\u7b97\u9ad8\u9636\u76f8\u5173\uff0c\u540e\u6765\u53d1\u73b0\u8fd9\u5bf9\u6781\u6027\u9ad8\u5206\u5b50\u6765\u8bf4\u662f\u4e0d\u53ef\u5ffd\u7565\u7684\u3002\u539f\u5b50\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u52bf\u6570\u636e\uff0c\u539f\u672c\u4e5f\u662f\u534a\u7ecf\u9a8c\u4f30\u7b97\u7684\uff1b\u518d\u5f80\u540e\uff0c\u91cf\u5b50\u5316\u5b66\u7b2c\u4e00\u6027\u539f\u7406\u65b9\u6cd5\u9010\u6e10\u6210\u719f\uff0c\u624d\u4f7f\u5f97\u201c\u76f8\u4e92\u4f5c\u7528\u52bf\u4ece\u5934\u7b97\u201d\u6210\u4e3a\u53ef\u80fd\uff0c\u8fd9\u662fFlory\u5f53\u5e74\u672a\u5fc5\u6765\u5f97\u53ca\u4eb2\u773c\u770b\u5230\u7684\u6f14\u8fdb\u3002 \u5f17\u6d1b\u91cc\u5c06\u9ad8\u5206\u5b50\u94fe\u7edf\u8ba1\u7269\u7406\u8fd9\u6761\u7814\u7a76\u8def\u7ebf\u4e00\u76f4\u63a8\u52a8\u5230\u4ed61985\u5e74\u53bb\u4e16\u3002\u8fd9\u6761\u8def\u7ebf\u4e0e\u540e\u6765\u76ae\u57c3\u5c14-\u5409\u52d2\u00b7\u5fb7\u70ed\u7eb3\uff08Pierre-Gilles de Gennes\uff09\u53d1\u5c55\u7684\u6807\u5ea6\u7406\u8bba\u662f\u5e76\u884c\u7684\u3001\u4e0d\u540c\u7684\u8def\u5f84\u3002\u8bb8\u591a\u573a\u5408\u4eba\u4eec\u559c\u6b22\u7528\u4e00\u79cd\u8bdd\u672f\u53d9\u8ff0\u5386\u53f2\uff1a\u201cFlory\u9884\u6d4bA\uff0c\u4f46\u6807\u5ea6\u7406\u8bba\u9884\u6d4bB\uff0c\u5b9e\u9a8c\u53d1\u73b0de Gennes\u5bf9\u201d\uff0c\u8fd9\u4f1a\u8ba9\u4e0d\u719f\u6089\u7684\u4eba\u8bef\u4ee5\u4e3a\u662f\u524d\u8005\u88ab\u540e\u8005\u5168\u9762\u63a8\u7ffb\u3002\u5728\u6211\u770b\u6765\uff0cde Gennes\u4e0e Edwards\u7b49\u4eba\u5728\u5f88\u591a\u5173\u952e\u95ee\u9898\u4e0a\u8fdb\u5165\u7684\u662fFlory\u5f53\u65f6\u6ca1\u6709\u8986\u76d6\u3001\u6216\u8005\u5f53\u65f6\u793e\u533a\u8fd8\u6ca1\u610f\u8bc6\u5230\u5fc5\u987b\u66f4\u65b0\u7269\u7406\u673a\u5236regime\u2014\u2014\u5c24\u5176\u662f\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u4e0d\u53ef\u5ffd\u7565\u3001\u51dd\u805a\u6001\u6548\u5e94\u4e0d\u53ef\u5ffd\u7565\u7684\u60c5\u5f62\uff0c\u4f8b\u5982\u534a\u6d53\u6eb6\u6db2\u7b49\u3002 \u800c\u4e14de Gennes\u7684\u4e00\u4e9b\u5173\u952e\u76f4\u89c9\u4e0e\u673a\u5236\uff0c\u548c\u6b27\u6d32\u6db2\u4f53\u7269\u7406\u7684\u53d1\u5c55\u8109\u7edc\u5173\u7cfb\u5f88\u6df1\uff1b\u4ed6\u5f53\u7136\u628a\u8fd9\u4e9b\u4e1c\u897f\u5e26\u8fdb\u4e86\u9ad8\u5206\u5b50\uff0c\u4f46\u628a\u8fd9\u6bb5\u6765\u6e90\u62b9\u5e73\u4e4b\u540e\uff0c\u5c31\u5bb9\u6613\u88ab\u8bb2\u6210\u201c\u5b8c\u5168\u539f\u521b\u3001\u51ed\u6807\u5ea6\u6280\u5de7\u5e73\u5730\u8d77\u9ad8\u697c\u201d\u3002Edwards\u65e9\u5e74\u5728Gee\u7684\u5f71\u54cd\u4e0b\u4ece\u6a61\u80f6\u5f39\u6027\u95ee\u9898\u8fdb\u5165\u9ad8\u5206\u5b50\u754c\uff0c\u6700\u521d\u7684\u52a8\u673a\u4e4b\u4e00\u4e0e\u89e3\u91caMooney\u2013Rivlin\u5f62\u5f0f\u91cc\u67d0\u4e9b\u53c2\u6570\uff08\u4f8b\u5982\u5e38\u88ab\u79f0\u4f5c\u00a0C2\u00a0\u7684\u90a3\u4e00\u9879\uff09\u4e3a\u4f55\u4e0d\u4e3a\u96f6\u6709\u5173\u3002 \u540e\u6765\u56f4\u7ed5\u201c\u7ea6\u675f\u201d\u7684\u8bed\u8a00\u4f53\u7cfb\u9010\u6e10\u4e30\u5bcc\uff1a\u7f20\u7ed3\u53ea\u662f\u7ea6\u675f\u7684\u4e00\u79cd\uff0c\u5c40\u57df\u7ea6\u675f\u8fd8\u4f1a\u5f15\u51fa\u66f4\u4e00\u822c\u7684\u975e\u5747\u5300\u6027\/\u5f02\u8d28\u6027\uff08heterogeneity\uff09\u8868\u8ff0\uff1b\u800cFlory\u81ea\u5df1\u66f4\u613f\u610f\u7ef4\u62a4\u4ed6\u4e0eErman\u5173\u4e8e\u201c\u4ea4\u8054\u70b9\u8fd0\u52a8\u53d7\u9650\u201d\u7684\u89e3\u91ca\u8def\u5f84\uff0c\u5e76\u4e0d\u8f7b\u6613\u5728\u8bed\u8a00\u4e0e\u6846\u67b6\u4e0a\u5411\u540e\u6765\u90a3\u5957\u6db2\u4f53\u7269\u7406\/\u76f8\u53d8\u7406\u8bba\u5316\u7684\u8868\u8ff0\u8ba9\u6b65\u3002\u8fd9\u7b97\u662fFlory\u76f4\u63a5\u5bf9\u201c\u4e0b\u4e00\u4e2a\u8303\u5f0f\u201d\u7684\u6709\u4ec0\u4e48\u76f4\u63a5\u53cd\u5e94\u7684\u4ec5\u6709\u8bb0\u5f55\u4e86\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":9332,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9332","url_meta":{"origin":9243,"position":5},"title":"\u9ad8\u5206\u5b50\u7269\u7406\u4e2d\u7684\u4e00\u4e9b\u65e5\u672c\u540d\u5b57","author":"Andrew","date":"2025\u5e7412\u670822\u65e5","format":false,"excerpt":"\u65e5\u672c\u7684\u73b0\u4ee3\u7269\u7406\u5316\u5b66 \u6c34\u5c9b\u4e09\u4e00\u90ce\uff08Mizushima Sanichiro\uff09\u5728Annu. Rev. Phys. Chem.\u4e0a\u4ecb\u7ecd\u65e5\u672c\u7269\u7406\u5316\u5b66\u7684\u5386\u53f2\uff0c\u52aa\u529b\u4ece\u65e5\u672c\u6587\u5316\u89e3\u91ca\uff0c\u4e3a\u4ec0\u4e48\u65e5\u672c\u7814\u7a76\u7684\u8bfe\u9898\u548c\u5bf9\u8c61\u8ddf\u897f\u65b9\u4e0d\u4e00\u6837\u3002\u4ed6\u4e5f\u63d0\u5230\u4e86\u4e2d\u56fd\u601d\u60f3\u5bb6\u600e\u4e48\u53cd\u601d\u4e3a\u4ec0\u4e48\u4e2d\u56fd\u6ca1\u6709\u4ea7\u751f\u73b0\u4ee3\u79d1\u5b66\u3002\u4ed6\u5f15\u7528\u4e86\u4efb\u9e3f\u96bd\u7684\u6587\u7ae0\uff0c\u4f46\u6709\u8da3\u7684\u662f\u4ed6\u597d\u50cf\u8bef\u4f1a\u4e86\u4efb\u662f\u4e00\u4f4d\u5973\u58eb\u3002\u6211\u624b\u5934\u4e0a\u6709\u4efb\u9e3f\u96bd\u7684\u6587\u96c6\uff0c\u4f46\u662f\u627e\u4e0d\u5230\u5355\u72ec\u7684\u4e00\u7bc7\u6587\u7ae0\u8868\u8ff0\u4e86\u6c34\u5c9b\u4e09\u4e00\u6717\u5f15\u8ff0\u7684\u6240\u6709\u5185\u5bb9\u3002\u5927\u81f4\u4e0a\uff0c\u6309\u7167\u6c34\u5c9b\u4e09\u4e00\u90ce\u7684\u5f15\u8ff0\uff0c\u5176\u4e2d\u4e00\u4e2a\u539f\u56e0\u662f\u4e2d\u56fd\u7684\u4e2d\u4e16\u7eaa\u6587\u5316\u8fc7\u4e8e\u5f3a\u8c03\u201dwhat to do over what to know\u201c\u3002\u6211\u89c9\u5f97\u8fd9\u4e2a\u63cf\u8ff0\u5341\u5206\u7cbe\u786e\u800c\u4e14\u60b2\u5267\u6027\u5730\u7edf\u6cbb\u81f3\u4eca\u3002\u4efb\u9e3f\u96bd\u786e\u5b9e\u5728\u300a\u5efa\u7acb\u5b66\u754c\u8bba\u300b\u4e2d\u8bf4\uff1a 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