{"id":4792,"date":"2012-07-14T07:17:32","date_gmt":"2012-07-13T23:17:32","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=4792"},"modified":"2020-02-04T23:50:16","modified_gmt":"2020-02-04T15:50:16","slug":"%e6%97%b6%e6%b8%a9%e5%8f%a0%e5%8a%a0%e5%be%97%e5%88%b0%e7%9a%84%e6%9d%be%e5%bc%9b%e6%97%b6%e9%97%b4%e6%98%af%e4%bb%80%e4%b9%88%e6%9d%be%e5%bc%9b%e6%97%b6%e9%97%b4%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4792","title":{"rendered":"\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u677e\u5f1b\u65f6\u95f4\u662f\u4ec0\u4e48\u677e\u5f1b\u65f6\u95f4\uff1f"},"content":{"rendered":"
\n

\u8fd9\u4e2a\u95ee\u9898\u641e\u4e86\u6211\u4e00\u4e2a\u901a\u5bb5\uff0c\u8bb0\u5f55\u4e00\u4e0b\u3002<\/p>\n

\u65f6\u6e29\u53e0\u52a0\u6027\u8d28\u662f\u6307\u4f53\u7cfb\u5728\u4e0d\u540c\u6e29\u5ea6\u6d4b\u91cf\u5f97\u5230\u7684\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u53ef\u5728\u65f6\u95f4\u8f74\u5e73\u79fb\u53e0\u52a0\u6210\u4e00\u6761\u4e3b\u66f2\u7ebf\u3002\u5e73\u79fb\u56e0\u5b50a<\/i>T<\/i><\/sub>\u5e38\u5e38\u8ba4\u4e3a\u662f\u677e\u5f1b\u65f6\u95f4\u7684\u6bd4\u503c\uff1a
\n\"a_T=\frac{\tau\left(T\right)}{\tau\left(T_\textup{ref}\right)}\"
\n\u4f46\u662f\uff0c\u5b9e\u9645\u6837\u54c1\u5f80\u5f80\u5177\u6709\u4e00\u4e2a\u8f83\u5bbd\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u3002\u90a3\u4e48\u4e0a\u5f0f\u4e2d\u7684\u677e\u5f1b\u65f6\u95f4\u5230\u5e95\u662f\u54ea\u4e2a\u503c\uff0c\u662f\u5e73\u5747\u503c\u8fd8\u662f\u6700\u5927\u503c\u8fd8\u662f\u4ec0\u4e48\uff1f<\/p>\n

\u73bb\u7483\u6001\u4f53\u7cfb\u7684\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u5e38\u5e38\u7b26\u5408Kohlrausch-Williams-Watts\uff08KWW\uff09\u5173\u7cfb\uff1a
\n\"G\left(t\right)=G_0\exp\left[-\left(\frac{t}{\tau_0}\right)^\beta\right]\"
\n\u5982\u679c\u4f53\u7cfb\u53ea\u6709\u4e00\u4e2a\u677e\u5f1b\u65f6\u95f4\u503c\uff0c\u5219\u03b2<\/i> = 1\uff0c\u03c4<\/i>0<\/sub>\u5c31\u662f\u677e\u5f1b\u65f6\u95f4\u3002\u5982\u679c0 < \u03b2<\/i> < 1\uff0c\u5219\u53cd\u6620\u4f53\u7cfb\u6709\u4e00\u4e2a\u5bbd\u5206\u5e03\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u3002\u03c4<\/i>0<\/sub>\u53ea\u80fd\u662f\u4e00\u4e2a\u7528\u6765\u63cf\u8ff0\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u7684\u7279\u5f81\u65f6\u95f4\u3002\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u5c31\u662f\u03c4<\/i>0<\/sub>\u7684\u6bd4\u503c\u3002\u03c4<\/i>0<\/sub>\u8ddf\u677e\u5f1b\u65f6\u95f4\u8c31\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u5b83\u662f\u4e0d\u662f\u5c31\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4<\/i>>\u5462\uff1f<\/p>\n

\u4ee5\u5e94\u529b\u677e\u5f1b\u4e3a\u4f8b\uff0c\u5047\u8bbe\u6837\u54c1\u53ef\u8868\u793a\u6210\u65e0\u6570\u4e2aMaxwell\u6a21\u578b\u7684\u548c\uff1a
\n\"G\left(t\right)=\int_0^\infty
\n\u5176\u4e2dg<\/i>(\u03c4<\/i>)\u662f\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u51fd\u6570\u3002\u5b83\u4e0e\u66f4\u5e38\u7528\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u5173\u7cfb\u662fH<\/i>(\u03c4<\/i>)=\u03c4g<\/i>(\u03c4<\/i>)\u3002\u7531\u4e8eG<\/i>(t<\/i>)\u7b26\u5408KWW\u65b9\u7a0b\uff0c\u5219\u6709
\n\"G\left(t\right)=\exp\left(-\frac{t}{\tau_0}\right)^\beta\"
\n\u4ee4u<\/i>=1\/\u03c4<\/i>\uff0c\u4e0a\u5f0f\u5c31\u53d8\u6210\u4e00\u4e2aLaplace\u53d8\u6362\uff1a
\n\"\int_0^\infty\exp\left(-ut\right)g\left(1\/u\right)du=\mathfrak{L}\left(\frac{g\left(\frac{1}{u}\right)}{u^2}\right)\"
\n\u4e3a\u4e86\u5f97\u5230g<\/i>(<\/i>\u03c4<\/i>)\uff0c\u987b\u8ba1\u7b97\u4ee5\u4e0b\u53cdLaplace\u53d8\u6362\uff1a
\n\"g\left(\tau\right)=\frac{1}{\tau^2}\mathfrak{L}^{-1}\left[\exp\left(-\frac{t}{\tau_0}\right)^\beta\right]\"
\ng<\/i>(\u03c4<\/i>)\u7684n<\/i>\u9636\u77e9<\u03c4n<\/sup><\/i>>\uff1a
\n\"\left<
\n\u6240\u4ee5
\n\"\left<
\n\u5373\u5bf9\u4e8e\u4e00\u4e2a\u6ee1\u8db3KWW\u578b\u54cd\u5e94\u51fd\u6570G<\/i>(t<\/i>)\u7684\u4f53\u7cfb\uff0c\u5176\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4<\/i>>\u4e0eKWW\u65b9\u7a0b\u7684\u7279\u5f81\u65f6\u95f4\u03c4<\/i>0<\/sub>\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u5e73\u79fb\u56e0\u5b50a<\/i>T<\/i><\/sub>\u786e\u5b9e\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4\u7684\u6bd4\u503c
\n\"a_T=\frac{\tau\left(T\right)}{\tau\left(T_\textup{ref}\right)}=\frac{\left<\u3002<\/p>\n

\u66f4\u9ebb\u70e6\u7684\u95ee\u9898\u662f\uff0c\u505a\u52a8\u6001\u6d4b\u8bd5\u7684\u65f6\u5019\uff0cG’<\/i> = G”<\/i>\u5904\u6240\u5bf9\u5e94\u7684\u9891\u7387\u5012\u6570\u662f\u4ec0\u4e48\u65f6\u95f4\uff1f\u5f88\u591a\u5730\u65b9\u8bf4\u8fd9\u662f\u6700\u5927\u677e\u5f1b\u65f6\u95f4\uff08maximum relaxation time\uff09\u03c4<\/i>m<\/sub>\uff0c\u5373\u5f53\u89c2\u5bdf\u65f6\u95f4\u65f6\u95f4\u8d85\u8fc7\u03c4<\/i>m<\/sub>\uff0c\u5c31\u53ef\u4ee5\u770b\u5230\u6837\u54c1\u7684\u6d41\u52a8\u3002\u53ef\u662f\uff0c\u4e00\u4e2a\u54cd\u5e94\u51fd\u6570\u7b26\u5408KWW\u65b9\u7a0b\u7684\u6837\u54c1\uff0c\u662f\u5426\u5177\u6709\u786e\u5b9a\u7684\u6700\u5927\u677e\u5f1b\u65f6\u95f4\uff1f\u4e5f\u5c31\u662f\u8bf4\uff0c\u5176\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u51fd\u6570g<\/i>(\u03c4<\/i>)\u662f\u5426\u6709\u786e\u5b9a\u7684\u5b9a\u4e49\u57df\uff0c\u4f7f\u5f97\u5f53\u03c4<\/i>>\u03c4<\/i>m<\/sub>\u65f6g<\/i>(\u03c4<\/i>) = 0\uff1f\u8fd9\u4e2a\u90fd\u4e0d\u597d\u8bf4\u3002\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u7684\u6982\u5ff5\u8ddf\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u5173\u7cfb\uff0c\u591a\u6570\u89c1\u4e8e\u4eba\u4e3a\u7ed9\u5b9a\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\uff0c\u4f8b\u5982Wedge-Box distribution\u3001BSW distribution\u7b49\u7b49\u3002\u7ed9\u5b9ag<\/i>(\u03c4<\/i>)\uff0c\u5012\u662f\u53ef\u4ee5\u5206\u522b\u8ba1\u7b97G’<\/i>\u548cG”<\/i>
\n\"G'\left(\omega\right)=\int_0^\infty
\n\"G''\left(\omega\right)=\int_0^\infty
\n\u4ee4G’<\/i> = G”<\/i>\uff0c\u628a\u4e0a\u9762\u4e24\u5f0f\u8054\u8d77\u6765\u89e3\u51fa\u03c9<\/i>\u6765\uff0c\u5c31\u80fd\u6c42\u5f97\u6240\u8c13\u7684\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u662f\u5565\uff0c\u4f46\u8fd9\u4e2a\u592a\u96be\u4e86\u2026\u2026\u53c8\u636e\u8bf4\uff0cG’<\/i> = G”<\/i>\u65f6\u7684\u03c9<\/i>\u4e5f\u5c31\u662fG”<\/i>\u6700\u5927\u503c\u65f6\u7684\u03c9<\/i>\u3002\u5219\u4e0a\u9762\u7b2c\u4e8c\u4e2a\u5f0f\u5b50\u6c42\u5bfc\uff0c\u5c31\u5269\u4e0b\u88ab\u79ef\u51fd\u6570\u4e86\u3002\u90a3\u5768\u4e1c\u897f\u4e2d\u53f3\u8fb9\u7684\u5206\u5f0f\u662f\u975e\u96f6\u7684\uff0c\u6240\u4ee5\u552f\u6709\u8ba9g<\/i>(\u03c4<\/i>)=0\u3002\u8fd9\u5c31\u53c8\u56de\u5230\u4e4b\u524d\u95ee\u7684\u90a3\u4e2a\u95ee\u9898\u4e86\uff1ag<\/i>(\u03c4<\/i>)\u662f\u5426\u6709\u786e\u5b9a\u7684\u5b9a\u4e49\u57df\uff0c\u4f7f\u5f97\u5f53\u03c4<\/i>>\u03c4<\/i>m<\/sub>\u65f6g<\/i>(\u03c4<\/i>) = 0\uff1f<\/p>\n

\u6709\u4eba\u7ed9\u51fa\uff08\u89c1\u53c2\u8003\u6587\u732e\uff09\u4e86g<\/i>(\u03c4<\/i>)\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff0c\u662f\u4e2a\u542bGamma\u51fd\u6570\u7684\u7ea7\u6570\u3002\u8981\u6211\u89e3g<\/i>(\u03c4<\/i>) = 0\u51e0\u4e4e\u662f\u4e0d\u53ef\u80fd\u7684\u2026\u2026<\/p>\n

\u8fd8\u6709\u4e00\u4e2a\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6cd5\uff0c\u5c31\u662f\u91c7\u7528\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u4e00\u4e9b\u8fd1\u4f3c\u7b97\u6cd5\u3002\u4f8b\u5982\uff1a
\n\"H\left(\tau\right)\approx-\left(\frac{1}{2.303}\right)\left.\left[\frac{dG\left(t\right)}{d\log
\n\u8fd9\u5c31\u53ef\u76f4\u63a5\u4eceG<\/i>(t<\/i>)\u53bb\u8ba1\u7b97\u677e\u5f1b\u65f6\u95f4\u8c31H<\/i>(\u03c4<\/i>)=\u03c4g<\/i>(\u03c4<\/i>)\uff0c\u7136\u540e\u4ee3\u5165\u4e0a\u9762\u7684\u5f0f\u5b50\u7b97\u51faG’<\/i>\u548cG”<\/i>\uff0c\u89e3\u51fa\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u6765\u3002\u4f46\u603b\u4e4b\u90a3\u4e24\u4e2a\u79ef\u5206\u8fd8\u662f\u5f88\u96be\u641e<\/p>\n

\u6211\u731c\u6d4b\u8ba1\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u03c4<\/i>m<\/sub>\u4e5f\u662f\u8ddf\u03c4<\/i>0<\/sub>\u548c\u03b2<\/i>\u6709\u5173\uff0c\u4f46\u662f\u5426\u6b63\u6bd4\u4e8e\u03c4<\/i>0<\/sub>\u5c31\u4e0d\u77e5\u9053\u4e86\u3002\u771f\u7684\u4e0d\u884c\u7684\u8bdd\uff0c\u6211\u53ea\u80fd\u5728MATLAB\u6570\u503c\u7b97\u4e00\u4e0b\uff0c\u8003\u5bdf\u4e00\u4e0b\u4e0d\u540c\u03b2<\/i>\u503c\u4e0b\u7684\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u03c4<\/i>m<\/sub>\u3001\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4<\/i>>\u548cKWW\u7684\u7279\u5f81\u65f6\u95f4\u03c4<\/i>0<\/sub>\u4e4b\u95f4\u7684\u8868\u89c2\u5173\u7cfb\uff0c\u770b\u80fd\u5426\u8fd1\u4f3c\u8ba4\u4e3a\u03c4<\/i>m<\/sub>\u8ddf\u03c4<\/i>0<\/sub>\u6210\u6b63\u6bd4\u3002\u5982\u679c\u80fd\uff0c\u5219\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u5e73\u79fb\u56e0\u5b50\uff0c\u540c\u65f6\u4e5f\u662f\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u4e4b\u6bd4\uff1a
\n\"a_T=\frac{\tau\left(T\right)}{\tau\left(T_\textup{ref}\right)}\approx\frac{\tau_\textup{m}\left(T\right)}{\tau_\textup{m}\left(T_\textup{ref}\right)}\"<\/p>\n

\u53c2\u8003\u6587\u732e\uff1aJ. Chem. Phys. 73:3348\uff0cText. Res. J. 21:404<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

\u8fd9\u4e2a\u95ee\u9898\u641e\u4e86\u6211\u4e00\u4e2a\u901a\u5bb5\uff0c\u8bb0\u5f55\u4e00\u4e0b\u3002 \u65f6\u6e29\u53e0\u52a0\u6027\u8d28\u662f\u6307\u4f53\u7cfb\u5728\u4e0d\u540c\u6e29\u5ea6\u6d4b\u91cf\u5f97\u5230\u7684\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u53ef\u5728\u65f6\u95f4\u8f74\u5e73\u79fb\u53e0\u52a0\u6210\u4e00\u6761\u4e3b\u66f2\u7ebf\u3002\u5e73\u79fb\u56e0\u5b50aT\u5e38\u5e38\u8ba4\u4e3a\u662f\u677e\u5f1b\u65f6\u95f4\u7684\u6bd4\u503c\uff1a \u4f46\u662f\uff0c\u5b9e\u9645\u6837\u54c1\u5f80\u5f80\u5177\u6709\u4e00\u4e2a\u8f83\u5bbd\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u3002\u90a3\u4e48\u4e0a\u5f0f\u4e2d\u7684\u677e\u5f1b\u65f6\u95f4\u5230\u5e95\u662f\u54ea\u4e2a\u503c\uff0c\u662f\u5e73\u5747\u503c\u8fd8\u662f\u6700\u5927\u503c\u8fd8\u662f\u4ec0\u4e48\uff1f \u73bb\u7483\u6001\u4f53\u7cfb\u7684\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u5e38\u5e38\u7b26\u5408Kohlrausch-Williams-Watts\uff08KWW\uff09\u5173\u7cfb\uff1a \u5982\u679c\u4f53\u7cfb\u53ea\u6709\u4e00\u4e2a\u677e\u5f1b\u65f6\u95f4\u503c\uff0c\u5219\u03b2 = 1\uff0c\u03c40\u5c31\u662f\u677e\u5f1b\u65f6\u95f4\u3002\u5982\u679c0 < \u03b2 < 1\uff0c\u5219\u53cd\u6620\u4f53\u7cfb\u6709\u4e00\u4e2a\u5bbd\u5206\u5e03\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u3002\u03c40\u53ea\u80fd\u662f\u4e00\u4e2a\u7528\u6765\u63cf\u8ff0\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u7684\u7279\u5f81\u65f6\u95f4\u3002\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u5c31\u662f\u03c40\u7684\u6bd4\u503c\u3002\u03c40\u8ddf\u677e\u5f1b\u65f6\u95f4\u8c31\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u5b83\u662f\u4e0d\u662f\u5c31\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4>\u5462\uff1f \u4ee5\u5e94\u529b\u677e\u5f1b\u4e3a\u4f8b\uff0c\u5047\u8bbe\u6837\u54c1\u53ef\u8868\u793a\u6210\u65e0\u6570\u4e2aMaxwell\u6a21\u578b\u7684\u548c\uff1a \u5176\u4e2dg(\u03c4)\u662f\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u51fd\u6570\u3002\u5b83\u4e0e\u66f4\u5e38\u7528\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u5173\u7cfb\u662fH(\u03c4)=\u03c4g(\u03c4)\u3002\u7531\u4e8eG(t)\u7b26\u5408KWW\u65b9\u7a0b\uff0c\u5219\u6709 \u4ee4u=1\/\u03c4\uff0c\u4e0a\u5f0f\u5c31\u53d8\u6210\u4e00\u4e2aLaplace\u53d8\u6362\uff1a \u4e3a\u4e86\u5f97\u5230g(\u03c4)\uff0c\u987b\u8ba1\u7b97\u4ee5\u4e0b\u53cdLaplace\u53d8\u6362\uff1a g(\u03c4)\u7684n\u9636\u77e9<\u03c4n>\uff1a \u6240\u4ee5 \u5373\u5bf9\u4e8e\u4e00\u4e2a\u6ee1\u8db3KWW\u578b\u54cd\u5e94\u51fd\u6570G(t)\u7684\u4f53\u7cfb\uff0c\u5176\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4>\u4e0eKWW\u65b9\u7a0b\u7684\u7279\u5f81\u65f6\u95f4\u03c40\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u5e73\u79fb\u56e0\u5b50aT\u786e\u5b9e\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4\u7684\u6bd4\u503c \u3002 \u66f4\u9ebb\u70e6\u7684\u95ee\u9898\u662f\uff0c\u505a\u52a8\u6001\u6d4b\u8bd5\u7684\u65f6\u5019\uff0cG’ = G”\u5904\u6240\u5bf9\u5e94\u7684\u9891\u7387\u5012\u6570\u662f\u4ec0\u4e48\u65f6\u95f4\uff1f\u5f88\u591a\u5730\u65b9\u8bf4\u8fd9\u662f\u6700\u5927\u677e\u5f1b\u65f6\u95f4\uff08maximum relaxation time\uff09\u03c4m\uff0c\u5373\u5f53\u89c2\u5bdf\u65f6\u95f4\u65f6\u95f4\u8d85\u8fc7\u03c4m\uff0c\u5c31\u53ef\u4ee5\u770b\u5230\u6837\u54c1\u7684\u6d41\u52a8\u3002\u53ef\u662f\uff0c\u4e00\u4e2a\u54cd\u5e94\u51fd\u6570\u7b26\u5408KWW\u65b9\u7a0b\u7684\u6837\u54c1\uff0c\u662f\u5426\u5177\u6709\u786e\u5b9a\u7684\u6700\u5927\u677e\u5f1b\u65f6\u95f4\uff1f\u4e5f\u5c31\u662f\u8bf4\uff0c\u5176\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u51fd\u6570g(\u03c4)\u662f\u5426\u6709\u786e\u5b9a\u7684\u5b9a\u4e49\u57df\uff0c\u4f7f\u5f97\u5f53\u03c4>\u03c4m\u65f6g(\u03c4) = 0\uff1f\u8fd9\u4e2a\u90fd\u4e0d\u597d\u8bf4\u3002\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u7684\u6982\u5ff5\u8ddf\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u5173\u7cfb\uff0c\u591a\u6570\u89c1\u4e8e\u4eba\u4e3a\u7ed9\u5b9a\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\uff0c\u4f8b\u5982Wedge-Box distribution\u3001BSW distribution\u7b49\u7b49\u3002\u7ed9\u5b9ag(\u03c4)\uff0c\u5012\u662f\u53ef\u4ee5\u5206\u522b\u8ba1\u7b97G’\u548cG” \u4ee4G’ = G”\uff0c\u628a\u4e0a\u9762\u4e24\u5f0f\u8054\u8d77\u6765\u89e3\u51fa\u03c9\u6765\uff0c\u5c31\u80fd\u6c42\u5f97\u6240\u8c13\u7684\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u662f\u5565\uff0c\u4f46\u8fd9\u4e2a\u592a\u96be\u4e86\u2026\u2026\u53c8\u636e\u8bf4\uff0cG’ = G”\u65f6\u7684\u03c9\u4e5f\u5c31\u662fG”\u6700\u5927\u503c\u65f6\u7684\u03c9\u3002\u5219\u4e0a\u9762\u7b2c\u4e8c\u4e2a\u5f0f\u5b50\u6c42\u5bfc\uff0c\u5c31\u5269\u4e0b\u88ab\u79ef\u51fd\u6570\u4e86\u3002\u90a3\u5768\u4e1c\u897f\u4e2d\u53f3\u8fb9\u7684\u5206\u5f0f\u662f\u975e\u96f6\u7684\uff0c\u6240\u4ee5\u552f\u6709\u8ba9g(\u03c4)=0\u3002\u8fd9\u5c31\u53c8\u56de\u5230\u4e4b\u524d\u95ee\u7684\u90a3\u4e2a\u95ee\u9898\u4e86\uff1ag(\u03c4)\u662f\u5426\u6709\u786e\u5b9a\u7684\u5b9a\u4e49\u57df\uff0c\u4f7f\u5f97\u5f53\u03c4>\u03c4m\u65f6g(\u03c4) = 0\uff1f \u6709\u4eba\u7ed9\u51fa\uff08\u89c1\u53c2\u8003\u6587\u732e\uff09\u4e86g(\u03c4)\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff0c\u662f\u4e2a\u542bGamma\u51fd\u6570\u7684\u7ea7\u6570\u3002\u8981\u6211\u89e3g(\u03c4) = 0\u51e0\u4e4e\u662f\u4e0d\u53ef\u80fd\u7684\u2026\u2026 \u8fd8\u6709\u4e00\u4e2a\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6cd5\uff0c\u5c31\u662f\u91c7\u7528\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u4e00\u4e9b\u8fd1\u4f3c\u7b97\u6cd5\u3002\u4f8b\u5982\uff1a \u8fd9\u5c31\u53ef\u76f4\u63a5\u4eceG(t)\u53bb\u8ba1\u7b97\u677e\u5f1b\u65f6\u95f4\u8c31H(\u03c4)=\u03c4g(\u03c4)\uff0c\u7136\u540e\u4ee3\u5165\u4e0a\u9762\u7684\u5f0f\u5b50\u7b97\u51faG’\u548cG”\uff0c\u89e3\u51fa\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u6765\u3002\u4f46\u603b\u4e4b\u90a3\u4e24\u4e2a\u79ef\u5206\u8fd8\u662f\u5f88\u96be\u641e \u6211\u731c\u6d4b\u8ba1\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u03c4m\u4e5f\u662f\u8ddf\u03c40\u548c\u03b2\u6709\u5173\uff0c\u4f46\u662f\u5426\u6b63\u6bd4\u4e8e\u03c40\u5c31\u4e0d\u77e5\u9053\u4e86\u3002\u771f\u7684\u4e0d\u884c\u7684\u8bdd\uff0c\u6211\u53ea\u80fd\u5728MATLAB\u6570\u503c\u7b97\u4e00\u4e0b\uff0c\u8003\u5bdf\u4e00\u4e0b\u4e0d\u540c\u03b2\u503c\u4e0b\u7684\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u03c4m\u3001\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4>\u548cKWW\u7684\u7279\u5f81\u65f6\u95f4\u03c40\u4e4b\u95f4\u7684\u8868\u89c2\u5173\u7cfb\uff0c\u770b\u80fd\u5426\u8fd1\u4f3c\u8ba4\u4e3a\u03c4m\u8ddf\u03c40\u6210\u6b63\u6bd4\u3002\u5982\u679c\u80fd\uff0c\u5219\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u5e73\u79fb\u56e0\u5b50\uff0c\u540c\u65f6\u4e5f\u662f\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u4e4b\u6bd4\uff1a \u53c2\u8003\u6587\u732e\uff1aJ. Chem. Phys. 73:3348\uff0cText. Res. J. 21:404<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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":[264,303],"tags":[],"class_list":["post-4792","post","type-post","status-publish","format-standard","hentry","category-264","category-rheo"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1aPvF-1fi","jetpack-related-posts":[{"id":4999,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4999","url_meta":{"origin":4792,"position":0},"title":"\u5bf9\u65f6X\u53e0\u52a0\u539f\u7406\u548c\u975e\u5e73\u8861\u8fc7\u7a0b\u7684\u4e00\u4e9b\u8ba4\u8bc6","author":"Andrew","date":"2012\u5e7411\u670811\u65e5","format":false,"excerpt":"\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u7684\u7a33\u5b9a\u6027\u662f\u600e\u4e48\u6765\u7684\uff1f 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superposition\u3002 Strain rate-frequency superposition 2007\u5e74Wyss\u7b49\u62a5\u9053\uff0c\u5728\u51e0\u79cd\u4e0d\u540c\u7684\u6d53\u80f6\u4f53\u4f53\u7cfb\u90fd\u5448\u73b0\u6240\u8c13strain rate-frequency 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\u90a3\u4e48\uff0c\u9002\u7528\u4e8e\u80f6\u4f53\u4f53\u7cfb\u7684\u6d41\u53d8\u5b66\u6a21\u578b\uff0c\u662f\u5426\u5c31\u90fd\u4e00\u5b9a\u80fd\u7b26\u5408SRFS\u5462\uff1f\u6211\u770b\u4e0d\u4e00\u5b9a\u3002\u4e5f\u8bb8\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u51fa\u53d1\uff0c\u53ef\u4ee5\u53bb\u8003\u5bdf\u8981\u6ee1\u8db3SRFS\u6d41\u53d8\u5b66\u6a21\u578b\u9700\u8981\u7b26\u5408\u4ec0\u4e48\u6837\u7684\u7279\u5f81\uff0c\u4ece\u800c\u53ef\u4ee5\u731c\u5230\u4e00\u4e9bSRFS\u7684\u672c\u8d28\uff0c\u540c\u65f6\u4e5f\u53ef\u4ee5\u770b\u770bSRFS\u53cd\u6620\u7684\u662f\u4ec0\u4e48\u201c\u7ed3\u6784\u677e\u5f1b\u201d\u3002\u8fd9\u9879\u5de5\u4f5c\u6211\u8fd8\u6ca1\u6709\u505a\uff0c\u56e0\u4e3a\u76ee\u524d\u63d0\u51fa\u7684\u80fd\u591f\u6bd4\u8f83\u5168\u9762\u5730\u63cf\u8ff0\u5c48\u670d\u5e94\u529b\u6d41\u4f53\u7684\u77ac\u6001\u6a21\u578b\u5e76\u4e0d\u591a\u3002\u8fd9\u6837\u7684\u672c\u6784\u65b9\u7a0b\u5f80\u5f80\u5c5e\u4e8estructural kinetic model\u7684\u7c7b\u578b\uff0c\u8bbe\u8ba1\u4e86\u5f88\u591a\u6ca1\u6709\u76f4\u63a5\u7269\u7406\u610f\u4e49\u7684\u8868\u8fbe\u5f0f\u51d1\u6765\u51d1\u53bb\u3002\u5982\u679c\u7528\u8fd9\u4e9b\u6a21\u578b\u53bb\u5c1d\u8bd5SRFS\uff0c\u65e0\u8bba\u662f\u6210\u8fd8\u662f\u4e0d\u6210\uff0c\u4f60\u90fd\u5f88\u96be\u83b7\u5f97\u4ec0\u4e48\u7269\u7406\u4e0a\u7684insight\u3002\u6240\u4ee5\uff0c\u6211\u5c31\u60f3\u6539\u7528\u4e00\u4e9b\u80f6\u4f53\u4f53\u7cfb\u7684first principle\u7684\u6d41\u53d8\u7406\u8bba\u3002\u9996\u5148\u60f3\u5230\u7684\u5c31\u662fMCT\u5411\u6d41\u53d8\u5b66\u7684\u63a8\u5e7f\uff0c\u5373Fuchs\u7b49\u4eba\u7684\u5de5\u4f5c\u3002\u5177\u4f53\u5730\uff0c\u662f\u5e0c\u671b\u91c7\u7528MCT-ITT\u7684\u4e00\u4e9b\u7b80\u5316\u7248schematic -model\u3002\u4f7f\u7528\u8fd9\u4e2a\u6a21\u578b\u6765\u9884\u6d4bLAOS\u7ed3\u679c\u7684\u62a5\u9053\u5df2\u7ecf\u6709\u4e86\u3002MCT-ITT\u7684\u6570\u5b66\u8fdc\u8fdc\u8d85\u8fc7\u4e86\u6211\u7684\u80fd\u529b\uff0c\u6211\u662f\u6700\u8fd1\u627e\u5230\u4e86\u4e00\u4e2a\u61c2\u6570\u5b66\u7684\u670b\u53cb\u5e2e\u5fd9\u8ba1\u7b97MCT\uff0c\u624d\u8003\u8651\u8fd9\u4e2a\u95ee\u9898\u7684\u3002\u8fd9\u9879\u5de5\u4f5c\u6b63\u5728\u8fdb\u884c\u4e2d\uff0c\u5b58\u5728\u4e00\u4e9b\u95ee\u9898\uff0c\u7a0d\u540e\u518d\u8bf4\u3002 \u8981\u56de\u7b54\u7b2c\u4e8c\u4e2a\u95ee\u9898\uff0c\u5373\u6709\u4ec0\u4e48\u6d41\u53d8\u5b66\u65b9\u6cd5\u80fd\u591f\u770b\u5230\u4f53\u7cfb\u5728\u975e\u7ebf\u6027\u6761\u4ef6\u4e0b\u7684\u7ed3\u6784\u677e\u5f1b\uff0c\u6211\u4eec\u5e94\u8be5\u9996\u5148\u628a\u60c5\u51b5\u7b80\u5316\u56de\u7a33\u6001\u526a\u5207\u3002\u8fb9\u8fdb\u884c\u7a33\u6001\u526a\u5207\uff0c\u8fb9\u8fdb\u884c\u677e\u5f1b\u6d4b\u8bd5\u7684\u6d41\u53d8\u5b66\u65b9\u6cd5\u662f\u6709\u7684\uff0c\u53eb\u505a\u201c\u53e0\u52a0\u6d41\u53d8\u5b66\u201d\uff0csuperposition rheology\u3002\u8fd9\u91cc\u7684superposition\u662f\u6307\u5728\u4e00\u4e2a\u7a33\u6001\u526a\u5207\u7684\u6d41\u573a\u4e0a\u53e0\u52a0\u4e00\u4e2a\u5c0f\u5e45\u632f\u8361\u7684\u6d41\u573a\u3002\u6837\u54c1\u7684\u54cd\u5e94\u53ef\u4ee5\u5206\u79bb\u6210\u7a33\u6001\u526a\u5207\u7684\u90e8\u5206\u548c\u5c0f\u5e45\u632f\u8361\u7684\u90e8\u5206\uff0c\u540e\u8005\u53ef\u4ee5\u6309\u7167\u7ebf\u6027\u54cd\u5e94\u7684\u505a\u6cd5\u5f97\u5230\u677e\u5f1b\u8c31\u3002\u4e00\u5171\u6709\u5e73\u884c\u548c\u6b63\u4ea4\u4e24\u79cd\u53e0\u52a0\u65b9\u6cd5\u3002\u6709\u62a5\u9053\u79f0\uff0c\u5e73\u884c\u53e0\u52a0\u7531\u4e8e\u8026\u5408\u7684\u56e0\u7d20\u5e76\u4e0d\u80fd\u83b7\u5f97\u771f\u6b63\u7684\u677e\u5f1b\u8c31\uff0c\u5fc5\u9762\u8981\u6b63\u4ea4\u53e0\u52a0\u7684\u624d\u53ef\u4ee5\u3002\u65e0\u8bba\u662f\u54ea\u79cd\u53e0\u52a0\uff0c\u90fd\u4e0d\u5bb9\u6613\u5728\u5546\u7528\u6d41\u53d8\u4eea\u4e0a\u5b9e\u73b0\u7684\uff0c\u9700\u8981\u8fdb\u884c\u6539\u9020\uff0c\u6240\u4ee5\u6211\u6682\u65f6\u4e0d\u80fd\u4eb2\u81ea\u505a\u8fd9\u6837\u7684\u5b9e\u9a8c\u3002\u6587\u732e\u62a5\u9053\u4e2d\u503c\u5f97\u7559\u610f\u7684\u6709\u5982\u4e0b\u8fd9\u4e9b\u3002\u5bf9\u9ad8\u5206\u5b50\u6eb6\u6db2\u505a\u4e86\u53e0\u52a0\u6d41\u53d8\u6d4b\u8bd5\uff0c\u53d1\u73b0\u6240\u5f97\u5230\u7684\u7ed3\u679c\u65e0\u6cd5\u8fdb\u884ctime-shear superposition\u3002\u5bf9\u805a\u4e59\u70ef\u7194\u4f53\u7684\u5b9e\u9a8c\u4e5f\u770b\u5230\u7c7b\u4f3c\u7684\u7ed3\u679c\u3002\u8fd9\u4e5f\u547c\u5e94\u4e86\u524d\u6587\u6240\u8bf4\u7f20\u7ed3\u4f53\u7cfb\u4e0d\u7b26\u5408SRFS\u7684\u73b0\u8c61\u3002\u80f6\u4f53\u4f53\u7cfb\u65b9\u9762\uff0c\u62a5\u9053\u4e86\u4e00\u4e9b\u672a\u53e0\u52a0\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c\u6211\u8fd8\u9700\u8981\u628a\u6587\u4e2d\u7684\u6570\u636e\u63d0\u53d6\u51fa\u6765\u5c1d\u8bd5\u53e0\u52a0\u6765\u9a8c\u8bc1\u4e00\u4e0b\u3002\u4f46\u662f\u5219\u51e0\u4e4e\u76f4\u63a5\u8bc1\u5b9e\u4e86time-shear superposition\u4e86\uff0c\u4f5c\u8005\u7ed9\u51fa\u4e86\u4e0d\u540c\u7a33\u6001\u5e94\u529b\u53e0\u52a0\u7684\u5c0f\u5e45\u626b\u9891\u66f2\u7ebf\uff0c\u5e76\u53e0\u52a0\u6210\u4e86\u4e3b\u66f2\u7ebf\uff0c\u4f46\u662f\u6ca1\u6709\u7ed9\u51fa\u76f8\u5e94\u7684\u526a\u5207\u901f\u7387\uff0c\u4e5f\u6ca1\u6709\u5bf9\u5e73\u79fb\u56e0\u5b50\u8fdb\u884c\u8ba8\u8bba\u3002\u4f46\u8fd9\u4e00\u62a5\u9053\u8bf4\u660e\uff0c\u80f6\u4f53\u4f53\u7cfb\u5728\u6d41\u53d8\u5b66\u884c\u4e3a\u4e0a\u4e5f\u662f\u7b26\u5408time-shear 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superposition\u5173\u7cfb\u5230\u03b2\u677e\u5f1b\u8fc7\u7a0b\u7684\u6807\u5ea6\u7279\u6027\u3002\u5bf9\u6b64\u8fdb\u884c\u4e86\u63a8\u5bfc\u3002\u5728\u73bb\u7483\u5316\u8f6c\u53d8\u9644\u8fd1\uff08\uff09\u5bc6\u5ea6\u76f8\u5173\u51fd\u6570\uff0c\u5176\u4e2dfq\u662fDebye-Waller factor\u3002\u5728MCT\u7684\u505a\u6cd5\u4e2d\uff0c\u4f3c\u4e4e\u89c4\u5b9a\u4e86b=1\u3002\u5176\u6b21\uff0c\u03c4\u4e0e\u7684\u5173\u7cfb\uff0c\u4e5f\u4f3c\u4e4e\u662f\u4eba\u4e3a\u89c4\u5b9a\u4e86\u7684\uff0c\u4f53\u73b0\u5728schematic -model\u7684memory function\u5f62\u5f0f\u7684\u9009\u62e9\u4e0a\uff1a \u8fd9\u662f\u5426\u8bf4\u660e\u54ea\u6015\u662fMCT\u7406\u8bba\u4e5f\u5e76\u6ca1\u6709\u9053\u51fatime-shear superposition\u7684\u7269\u7406\u5b9e\u8d28\uff1f\u2026","rel":"","context":"In 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