{"id":9238,"date":"2025-07-30T21:31:12","date_gmt":"2025-07-30T13:31:12","guid":{"rendered":"https:\/\/www.andrewsun.net\/panta_rhei\/?p=9238"},"modified":"2025-07-30T21:31:12","modified_gmt":"2025-07-30T13:31:12","slug":"p-flory%e8%87%aa%e8%bf%b0%e5%af%b9m-huggins%e5%b7%a5%e4%bd%9c%e7%9a%84%e9%a6%96%e6%ac%a1%e5%85%b3%e6%b3%a8","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9238","title":{"rendered":"P. Flory\u81ea\u8ff0\u5bf9M. Huggins\u5de5\u4f5c\u7684\u9996\u6b21\u5173\u6ce8"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"9238\">\n\n<p>\u805a\u5408\u7269\u6eb6\u6db2\u7684Flory&#8211;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\u662f<a href=\"https:\/\/en.wikipedia.org\/wiki\/Maurice_Loyal_Huggins\" target=\"_blank\" rel=\"noreferrer noopener\">Maurice L. Huggins<\/a>\u5148\u505a\u7684\u3002\u4ece\u53d1\u8868\u7684\u65f6\u95f4\u6765\u770b\uff0cHuggins\u53d1\u8868\u4e8e1941\u5e745\u6708<span id=\"cite_ITEM-9238-0\" name=\"citation\"><a href=\"#ITEM-9238-0\">[1]<\/a><\/span>\uff0cFlory\u53d1\u8868\u4e8e\u540c\u5e748\u6708<span id=\"cite_ITEM-9238-1\" name=\"citation\"><a href=\"#ITEM-9238-1\">[2]<\/a><\/span>\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. Bancroft Colloid Symposium\u4e0a\uff0cHuggins\u62a5\u544a\u4e86\u4ed6\u7684\u5de5\u4f5c\u3002\u591a\u5e74\u4e4b\u540e\u76841985\u5e74\uff0cFlory\u7684\u540e\u4e00\u7bc71942\u5e74\u7684\u8bba\u6587<span id=\"cite_ITEM-9238-2\" name=\"citation\"><a href=\"#ITEM-9238-2\">[3]<\/a><\/span>\u88ab\u7f8e\u56fd\u79d1\u5b66\u4fe1\u606f\u7814\u7a76\u6240\uff08Institutide of Scientific Information\uff0cISI\uff09\u7684\u671f\u520a<em>Current Contents<\/em>\u9009\u4e3a\u201c\u672c\u5468\u7ecf\u5178\u5f15\u7528\u201d\uff081985\u5e745\u67086\u65e5\uff0c\u7b2c18\u671f\uff09\uff0c\u8fd9\u4e2a\u680f\u76ee\u4f1a\u9080\u8bf7\u8bba\u6587\u4f5c\u8005<a href=\"https:\/\/garfield.library.upenn.edu\/classics1985\/A1985AFW3100001.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u5199\u70b9\u6545\u4e8b<\/a>\u3002Flory\u5728\u8fd9\u91cc\u4eb2\u81ea\u56de\u5fc6\u4e86\u4ed6\u5728Wilder D. Bancroft Colloid Symposium\u9996\u6b21\u5f97\u77e5Huggins\u505a\u4e86\u8ddf\u4ed6\u91cd\u590d\u7684\u5de5\u4f5c\u7684\u5f88\u591a\u7ec6\u8282\u3002Huggins\u662fLewis\u7684\u5b66\u751f\uff0c\u662fFlory\u7684\u524d\u8f88\u3002\u4ee5\u4e0b\u662fFlory\u56de\u5fc6\u7684\u4e00\u6bb5\u539f\u6587\u7684\u4e2d\u6587\u8bd1\u6587\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u6211\u4eec\u7684\u7814\u7a76\u662f\u72ec\u7acb\u8fdb\u884c\u7684\u3002\u6211\u7b2c\u4e00\u6b21\u4e86\u89e3\u5230Huggins\u7684\u5de5\u4f5c\uff0c\u662f\u57281941\u5e746\u6708\u4e8e\u5eb7\u5948\u5c14\u5927\u5b66\u4e3e\u884c\u7684\u80f6\u4f53\u7814\u8ba8\u4f1a\u4e0a\uff0c\u5f53\u65f6\u4ed6\u5c55\u793a\u4e86\u4ed6\u7684\u7814\u7a76\u6210\u679c\u3002\u5728\u90a3\u6b21\u7814\u8ba8\u4f1a\u4e0a\uff0c\u6211\u53d1\u8868\u4e86\u4e00\u7bc7\u5173\u4e8e\u975e\u7ebf\u5f62\u805a\u5408\u7269\u51dd\u80f6\u5316\u548c\u7f51\u7edc\u5f62\u6210\u7406\u8bba\u7684\u8bba\u6587\uff0c\u8fd9\u4e2a\u4e3b\u9898\u4e0e\u4e0a\u8ff0\u5185\u5bb9\u65e0\u5173\uff0c\u4f46\u50cf\u5b83\u4e00\u6837\uff0c\u4e5f\u83b7\u5f97\u4e86\u5e7f\u6cdb\u7684\u8ba4\u53ef\u3002\u4eceHuggins\u7684\u6f14\u8bb2\u4e2d\uff0c\u6211\u60ca\u8bb6\u5730\u5f97\u77e5\u4ed6\u6240\u8fdb\u884c\u7684\u5de5\u4f5c\u4e0e\u6211\u5f53\u65f6\u6b63\u51c6\u5907\u53d1\u8868\u7684\u5173\u4e8e\u805a\u5408\u7269\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u7814\u7a76\u975e\u5e38\u76f8\u4f3c\u3002\u6f14\u8bb2\u7ed3\u675f\u540e\uff0c\u6211\u8d70\u8fd1\u4ed6\uff0c\u6307\u51fa\u6211\u4e5f\u5728\u8fdb\u884c\u7c7b\u4f3c\u7684\u7814\u7a76\u3002\u4ed6\u975e\u5e38\u548c\u853c\uff0c\u9f13\u52b1\u6211\u8fd9\u4e2a\u5f53\u65f6\u8fd8\u53ea\u662f\u4e2a\u65e0\u540d\u5c0f\u5352\u7684\u4eba\u53d1\u8868\u6211\u7684\u5de5\u4f5c\uff0c\u5e76\u4e0e\u4ed6\u4ea4\u6d41\u3002\u8fd9\u662f\u6211\u4eec\u7684\u7b2c\u4e00\u6b21\u4f1a\u9762\uff0c\u4e5f\u5f00\u542f\u4e86\u6211\u4eec\u4e00\u751f\u7684\u53cb\u8c0a\u3002\u540e\u6765\uff0c\u6211\u4eec\u5c31\u5404\u79cd\u4e3b\u9898\u548c\u53d1\u5c55\u8fdb\u884c\u4e86\u8bb8\u591a\u79d1\u5b66\u8ba8\u8bba,\u867d\u7136\u5e76\u4e0d\u603b\u662f\u5b8c\u5168\u4e00\u81f4\uff0c\u4f46\u603b\u662f\u76f8\u4e92\u5c0a\u91cd\uff0c\u5173\u7cfb\u878d\u6d3d\u3002\u6b63\u5982\u6211\u5e38\u8bf4\u7684\uff0c\u4ee5\u6211\u4eec\u540d\u5b57\u547d\u540d\u7684\u8fd9\u4e2a\u7406\u8bba\uff0c\u6211\u4eec\u7684\u540d\u5b57\u987a\u5e8f\u5e94\u8be5\u98a0\u5012\u8fc7\u6765\uff0c\u56e0\u4e3a\u4ed6\u7684\u7b2c\u4e00\u7bc7\u8bba\u6587\u6bd4\u6211\u7684\u65e9\u4e86\u4e00\u4e24\u4e2a\u6708\u3002\u4ed6\u6700\u521d\u7684\u8d21\u732e\u66f4\u8be6\u7ec6\u5730\u9610\u8ff0\u4e86\u6676\u683c\u7406\u8bba\uff0c\u800c\u6211\u7684\u53ef\u80fd\u5728\u67d0\u4e9b\u65b9\u9762\u66f4\u5168\u9762\u3002<\/p>\n<\/blockquote>\n\n\n\n<p><\/p>\n<h2>References<\/h2>\n    <ol>\n    <li><a name='ITEM-9238-0'><\/a>\nM.L. Huggins, \"Solutions of Long Chain Compounds\", <i>The Journal of Chemical Physics<\/i>, vol. 9, pp. 440-440, 1941. <a href=\"http:\/\/dx.doi.org\/10.1063\/1.1750930\">http:\/\/dx.doi.org\/10.1063\/1.1750930<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9238-1'><\/a>\nP.J. Flory, \"Thermodynamics of High Polymer Solutions\", <i>The Journal of Chemical Physics<\/i>, vol. 9, pp. 660-660, 1941. <a href=\"http:\/\/dx.doi.org\/10.1063\/1.1750971\">http:\/\/dx.doi.org\/10.1063\/1.1750971<\/a>\n\n\n<\/li>\n<li><a name='ITEM-9238-2'><\/a>\nP.J. Flory, \"Thermodynamics of High Polymer Solutions\", <i>The Journal of Chemical Physics<\/i>, vol. 10, pp. 51-61, 1942. <a href=\"http:\/\/dx.doi.org\/10.1063\/1.1723621\">http:\/\/dx.doi.org\/10.1063\/1.1723621<\/a>\n\n\n<\/li>\n<\/ol>\n\n<\/div> <!-- kcite-section 9238 -->","protected":false},"excerpt":{"rendered":"<p>\u805a\u5408\u7269\u6eb6\u6db2\u7684Flory&#8211;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. Bancroft Colloid Symposium\u4e0a\uff0cHuggins\u62a5\u544a\u4e86\u4ed6\u7684\u5de5\u4f5c\u3002\u591a\u5e74\u4e4b\u540e\u76841985\u5e74\uff0cFlory\u7684\u540e\u4e00\u7bc71942\u5e74\u7684\u8bba\u6587\u88ab\u7f8e\u56fd\u79d1\u5b66\u4fe1\u606f\u7814\u7a76\u6240\uff08Institutide of Scientific Information\uff0cISI\uff09\u7684\u671f\u520aCurrent Contents\u9009\u4e3a\u201c\u672c\u5468\u7ecf\u5178\u5f15\u7528\u201d\uff081985\u5e745\u67086\u65e5\uff0c\u7b2c18\u671f\uff09\uff0c\u8fd9\u4e2a\u680f\u76ee\u4f1a\u9080\u8bf7\u8bba\u6587\u4f5c\u8005\u5199\u70b9\u6545\u4e8b\u3002Flory\u5728\u8fd9\u91cc\u4eb2\u81ea\u56de\u5fc6\u4e86\u4ed6\u5728Wilder D. Bancroft Colloid Symposium\u9996\u6b21\u5f97\u77e5Huggins\u505a\u4e86\u8ddf\u4ed6\u91cd\u590d\u7684\u5de5\u4f5c\u7684\u5f88\u591a\u7ec6\u8282\u3002Huggins\u662fLewis\u7684\u5b66\u751f\uff0c\u662fFlory\u7684\u524d\u8f88\u3002\u4ee5\u4e0b\u662fFlory\u56de\u5fc6\u7684\u4e00\u6bb5\u539f\u6587\u7684\u4e2d\u6587\u8bd1\u6587\u3002 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x_1+n_2\\ln x_2\\right]$$\u800cFlory--Huggins\u7406\u8bba\u7ed9\u51fa\u7684\u5c0f\u5206\u5b50\u6eb6\u5242+\u7ebf\u5f62\u9ad8\u805a\u7269\u6eb6\u8d28\u7684\u7ed3\u679c\u662f\uff1a$$\\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--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--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 A. Miller (1948), The Theory of Solutions of High Polymers, Clarendon E. Guggenheim (1952), Mixtures, Clarendon\u4e5f\u53ef\u4ee5\u53c2\u8003H. Tompa\u7684\u4e66\uff1a H. Tompa (1956), Polymer Solutions, Butterworths \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--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--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--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\u2026","rel":"","context":"In &quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8394,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8394","url_meta":{"origin":9238,"position":1},"title":"Yakov Ilyich Frenkel","author":"Andrew","date":"2022\u5e745\u670815\u65e5","format":false,"excerpt":"\u4ea4\u8054\u805a\u5408\u7269\u7f51\u7edc\u6eb6\u80c0\u7684\u70ed\u529b\u5b66\u72b6\u6001\u65b9\u7a0b\uff0cFlory\u2013Rehner\u65b9\u7a0b\uff0c\u5e38\u5e38\u4e5f\u88ab\u79f0\u4e3aFrenkel\u2013Flory\u2013Rehner\u65b9\u7a0b\u3002\u8fd9\u91cc\u7684Frenkel\u662f\u4fc4\u56fd\/\u524d\u82cf\u8054\u7269\u7406\u5b66\u5bb6Yakov Ilyich Frenkel\u3002\u5173\u4e8e\u8fd9\u4f4d\u7269\u7406\u5b66\u5bb6\u7684\u4ecb\u7ecd\u6709\u5f88\u591a\uff1a Jacov Il'ich Frenkel (1894 - 1952) - Biography - MacTutor History of Mathematics (st-andrews.ac.uk)Frenkel, Jacob Ilyich (imtqy.com)Biography:Yakov Frenkel - HandWikiYakov Il'ich Frenkel: Physics Today: Vol 47, No 6 (scitation.org)Viktor Yakovlevich Frenkel: Physics Today: Vol 50, No 7 (scitation.org) \u4ed6\u628a\u521d\u8bde\u65f6\u671f\u7684\u91cf\u5b50\u529b\u5b66\u6700\u65b0\u8fdb\u5c55\u5e26\u56de\u4e86\u5217\u5b81\u683c\u52d2\u3002\u6717\u9053\u5c31\u662f\u4ed6\u6700\u65e9\u7684\u5b66\u751f\u4e4b\u4e00\u3002Frenkel\u7684\u4e3b\u8981\u6210\u679c\u4e5f\u662f\u5728\u7535\u52a8\u529b\u5b66\u3001\u91cf\u5b50\u529b\u5b66\u548c\u51dd\u805a\u6001\u7269\u7406\u3002\u5728\u4e0a\u5217\u5bf9\u4ed6\u7684\u4e00\u822c\u4ecb\u7ecd\u5f53\u4e2d\uff0c\u51e0\u4e4e\u90fd\u6ca1\u6709\u63d0\u5230\u4ed6\u5bf9\u9ad8\u5206\u5b50\u7269\u7406\u7684\u6d89\u8db3\u3002Frenkel\u2013Flory\u2013Rehner\u65b9\u7a0b\u4e4b\u6240\u4ee5\u51a0\u4ed6\u7684\u540d\u5b57\u662f\u6765\u81ea\u4ed6\u57281938\u5e74\u53d1\u8868\u7684\u8bba\u6587\u3002\u8fd9\u7bc7\u8bba\u6587\u7684\u9898\u76ee\u7279\u522b\u50cf\u4e00\u672c\u6bd4\u8f83\u5b8c\u6574\u7684\u9ad8\u5206\u5b50\u7269\u7406\u4e66\uff0c\u4f46\u5b9e\u9645\u4e0a\u5bf9\u4e8e\u6807\u9898\u4e2d\u7684\u6bcf\u4e00\u4e2a\u8bdd\u9898\uff0cFrenkel\u90fd\u53ea\u4ece\u6700\u7b80\u5355\u7684\u7269\u7406\u76f4\u89c9\u51fa\u53d1\u63a8\u5bfc\u51fa\u4e00\u4e9b\u7ed3\u8bba\u3002\u8fd9\u662f\u786e\u5b9e\u662fFrenkel\u672c\u4eba\u7684\u98ce\u683c\uff0c\u8bb8\u591a\u5bf9\u4ed6\u7684\u4ecb\u7ecd\u90fd\u4e0d\u7ea6\u800c\u540c\u5730\u6279\u8bc4\u4ed6\u8fd9\u4e00\u70b9\u3002\u4f8b\u5982Phys. Today\u7684\u6587\u7ae0\u8bf4\uff1a He wrote with great clarity, using simple\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":9238,"position":2},"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. 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Flory\u57281951\u5e74\u7684\u95fb\u540d\u8457\u4f5c Principles of Polymer Chemistry \u4e2d\u663e\u793a\u51fa\u7684\u70ed\u529b\u5b66\u7684\u7edf\u8ba1\u529b\u5b66\u65b9\u6cd5\uff0c\u57fa\u672c\u4e0a\u8fd8\u662f\u8fd9\u4e24\u4e2a\u5b66\u79d11950\u5e74\u4e4b\u524d\u7684\u5f62\u6001\u3002\u5f53\u4ed6\u79bb\u5f00\u5eb7\u5948\u5c14\u5927\u5b66\u4e4b\u540e\uff081960s ~ 70s\uff09\uff0c\u65e0\u8bba\u662f\u70ed\u529b\u5b66\u8fd8\u662f\u7edf\u8ba1\u529b\u5b66\u7684\u5de5\u4f5c\u90fd\u5438\u6536\u4e86\u8fd9\u4e24\u4e2a\u5b66\u79d1\u7684\u8fd1\u4e16\u5316\u6210\u679c\u3002\u4f46\u90fd\u53ea\u4f53\u73b0\u5728\u4ed6\u540e\u6765\u53d1\u8868\u7684\u8bba\u6587\u5f53\u4e2d\u3002\u800c\u518d\u6ca1\u6709\u603b\u7ed3\u6210\u4e00\u672c\u50cf1951\u5e74\u8fd9\u672c\u4e66\u90a3\u6837\u5bf9\u5b66\u79d1\u672c\u79d1\u6559\u5b66\u5f71\u54cd\u6df1\u8fdc\u7684\u65b0\u4e66\u3002\u73b0\u5728\u7684\u9ad8\u5206\u5b50\u7269\u7406\u672c\u79d1\u6559\u6750\uff0c\u57fa\u672c\u6ca1\u6709\u516d\u3001\u4e03\u5341\u5e74\u4ee3\u7684\u4e1c\u897f\uff0c\u5b8c\u5168\u662fFlory1951\u5e74\u8fd9\u672c\u4e66\u7684\u590d\u523b\uff0c\u751a\u81f3\u8fd8\u4e22\u5931\u4e86Flory\u539f\u4e66\u4e2d\u5f88\u591a\u5145\u6ee1\u7269\u7406\u6d1e\u89c1\u7684\u53d9\u8ff0\uff08\u56e0\u4e3a\u8bd1\u8005\u770b\u4e0d\u61c2\uff09\u3002 \u683c\u5b50\u6a21\u578b\u7528\u4e8e\u6db2\u4f53 \u867d\u7136Kirkwood\uff0cOnsager\u7684\u5de5\u4f5c\u53ef\u4ee5\u8ffd\u6eaf\u523030\u5e74\u4ee3\uff0c\u4f46\u8fd9\u4e9b\u5de5\u4f5c\u65e0\u8bba\u662f\u5bf9\u975e\u5e73\u8861\u7684\u70ed\u529b\u5b66\/\u7edf\u8ba1\u529b\u5b66\uff0c\u8fd8\u662f\u5bf9\u6db2\u4f53\u7269\u7406\u7684\u5f71\u54cd\uff0c\u90fd\u8981\u523060\u5e74\u4ee3\u5de6\u53f3\u624d\u88ab\u516c\u8ba4\u3002\u800c\u4e14Flory\u5173\u5fc3\u7684\u95ee\u9898\u4e5f\u4e3b\u8981\u4ece\u5e73\u8861\u6001\u5207\u5165\u3002\u5728\u8fd9\u65b9\u9762\u572850\u5e74\u4ee3\u5df2\u7ecf\u5f62\u6210\u5341\u5206\u6210\u719f\u7684\u7406\u8bba\u5de5\u5177\u3002\u5176\u4e2d\u70ed\u529b\u5b66\u5f53\u65f6\u7684\u8868\u73b0\u5f62\u5f0f\u5c31\u8ddf\u4eca\u5929\u672c\u79d1\u300a\u7269\u7406\u5316\u5b66\u300b\u4e2d\u7684\u5dee\u4e0d\u591a\u3002\u800c\u7edf\u8ba1\u529b\u5b66\u7684\u8868\u73b0\u5f62\u5f0f\u53ef\u4ee5\u7528Fowler & Guggenheim (1949), Statistical Thermodynamics, CUP\u6765\u4ee3\u8868\u3002\u8fd9\u672c\u4e66\u9996\u5370\u662f1939\u5e74\uff0c1949\u5e74\u6709\u4e00\u4e2a\u4fee\u8ba2\u7248\uff0c\u4e4b\u540e\u5c31\u53ea\u6709\u91cd\u5370\uff0c\u6ca1\u6709\u65b0\u7248\u3002\u8fd9\u672c\u4e66\u5728\u5f53\u65f6\u662f\u5341\u5206\u6d41\u884c\u7684\u53c2\u8003\u4e66\u3002\u8be5\u4e66\u7684\u4e00\u4e2a\u7279\u70b9\u662f\u6709\u597d\u51e0\u4e2a\u5173\u6ce8\u4eca\u5929\u6240\u8c13\u7684\u8f6f\u51dd\u805a\u6001\u4f53\u7cfb\u7684\u5e94\u7528\u7ae0\u8282\u2014\u2014\u6db2\u4f53\u7eaf\u7269\u8d28\u548c\u6df7\u5408\u7269\u548c\u754c\u9762\u95ee\u9898\u3002\u81f3\u5c11\uff0c\u6db2\u4f53\u7684\u957f\u7a0b\u65e0\u5e8f\u7279\u70b9\u4ee5\u201c\u5f84\u5411\u5206\u5e03\u51fd\u6570\u201d\u8fd9\u79cd\u56fe\u50cf\u5df2\u88ab\u719f\u77e5\u3002 Flory\u539f\u4e66\u5728\u521a\u4e00\u629b\u51fa\u201c\u683c\u5b50\u6a21\u578b\u201d\u7684\u65f6\u5019\uff0c\u5c31\u63d2\u5165\u4e86\u4e00\u6bb5\u8bc4\u8ff0\uff1a The molecules in the pure liquids and in their solution are considered 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TSEPOCHKI\uff08\u805a\u5408\u7269\u94fe\u7684\u5f1b\u8c6b\u8c31\u7406\u8bba\uff09\u7684\u5de5\u4f5c\u3002\u4ed6\u662f\u7b2c\u4e00\u4f5c\u8005\uff0c\u7b2c\u4e8c\u4f5c\u8005\u662fM. V. Volkenstein\u3002 \u4e0d\u5931\u516c\u5e73\u5730\u53ef\u4ee5\u8bf4Volkenstein\u6bd4\u66f4\u8457\u540d\u4e9b\uff0c\u4f46\u53ef\u80fd\u4eca\u5929\u7684\u9ad8\u5206\u5b50\u5b66\u8005\u4e5f\u672a\u5fc5\u4e86\u89e3\u4e86\u3002Volkenstein\u7406\u5e94\u8457\u540d\uff0c\u56e0\u4e3aFlory\u5728\u8bfa\u8d1d\u5c14\u5956\u7f51\u7ad9\u4e0a\u7684\u81ea\u8ff0\u4e2d\u5c31\u63d0\u5230\uff0c\u4ed6\u7684\u5de5\u4f5c\u5efa\u7acb\u5728Volkenstein\u7684\u57fa\u7840\u4e0a\u7684\u3002Volkenstein\u5728\u952e\u6784\u8c61\u7edf\u8ba1\u65b9\u9762\u7684\u5de5\u4f5c\uff0c\u6bd4Flory\u5f00\u5c55\u5f97\u65e9\u3002Flory\u7684\u4e13\u8457Statistical Mechanics of Chain Molecules\u51fa\u7248\u540e\uff0cVolkenstein\u5728Biopolymers\u4e0a\u53d1\u8868\u4e86\u4e66\u8bc4\uff0c\u89c1\u8bc1\u4e86\u4e24\u4e2a\u5de8\u4eba\u7684\u4ea4\u6d41\u3002\u76f8\u4fe1\u8fd9\u662f\u8fd9\u4e2a\u4eca\u5929\u5c11\u6709\u4eba\u77e5\u5374\u6e0a\u6e90\u6df1\u8fdc\u7684\u671f\u520a\u4e0a\u4e3a\u6570\u4e0d\u5c11\u7684\u9ad8\u5149\u65f6\u523b\u4e4b\u4e00\u3002 \u5728\u8fd9\u91cc\u6211\u63d2\u4e00\u53e5\u3002\u4ece\u6211\u7684\u89c2\u5bdf\u6765\u770b\uff0c\u6211\u6000\u7591\uff0c\u8bb8\u591a\u4eba\u5e76\u6ca1\u6709\u770b\u8fc7Flory\u7684\u90a3\u672cStatistical Mechanics of Chain Molecules\u5c31\u53bb\u5f15\u7528\u3002\u8fd9\u672c\u4e66\u6709\u5341\u5206\u72ec\u7acb\u4e14\u4eca\u5929\u7f55\u89c1\u7684\u4e3b\u65e8\uff0c\u662f\u8d85\u51fa\u4e86\u4e00\u822c\u9ad8\u5206\u5b50\u7269\u7406\u6559\u79d1\u4e66\u4e2d\u7684\u94fe\u7edf\u8ba1\u7ae0\u8282\uff08\u5305\u62ecFlory\u672c\u4eba\u7684\u53e6\u4e00\u66f4\u4e3a\u6d41\u884c\u7684\u8457\u4f5cPrinciple of Polymer Chemistry\uff09\u6240\u5173\u5fc3\u7684\u8303\u7574\u7684\u3002Flory\u5728Statistical ~\u8fd9\u672c\u4e66\u4e2d\u4e3a\u4e86\u5b9e\u73b0\u4ed6\u6240\u4e0d\u540c\u4e8eKuhn\u7684\u7406\u8bba\u76ee\u6807\uff0c\u4f7f\u7528\u4e86\u5c11\u89c1\u4e8e\u5e38\u89c4\u6559\u79d1\u4e66\u7684\u6570\u5b66\u5de5\u5177\u3002\u6709\u65f6\u95f4\u6211\u518d\u53e6\u5916\u5199\u4e00\u7bc7\u4e1c\u897f\u6765\u804a\u804a\u8fd9\u4ef6\u4e8b\u3002 \u4f46\u65e0\u5eb8\u7f6e\u7591\uff0c\u8fd9\u672c\u4e66\u6b63\u9762\u5f15\u7528\u4e86\u4e0d\u5c11Volkenstein\u7684\u5de5\u4f5c\uff0c\u4f7f\u540e\u8005\u5341\u5206\u5f00\u5fc3\u3002 \u4e4b\u6240\u4ee5\u8bf4\u671f\u520aBiopolymers\u6709\u4e0d\u5c11\u9ad8\u5149\u65f6\u523b\uff0c\u662f\u56e0\u4e3a\u5b83\u6df1\u5ea6\u53c2\u4e0e\u4e86\u9ad8\u5206\u5b50\u7269\u7406\u7406\u8bba\u53d1\u5c55\u53f2\u7684\u4e3b\u7ebf\uff0c\u5f88\u591a\u91cd\u8981\u7684\u9ad8\u5206\u5b50\u7269\u7406\u57fa\u672c\u95ee\u9898\uff0c\u662f\u7269\u7406\u5b66\u5bb6\u5728\u7814\u7a76\u751f\u7269\u5927\u5206\u5b50\u7684\u65f6\u5019\u78b0\u5230\u7684\uff0c\u5f53\u65f6\u4ed6\u4eec\u628a\u8fd9\u4e9b\u5de5\u4f5c\u53d1\u8868\u5728\u4e86Biopolymers\uff0c\u540e\u6765\u6210\u4e3a\u4e86\u91cd\u8981\u7684\u666e\u9002\u7406\u8bba\u3002Volkenstein\u672c\u4eba\u5c31\u5341\u5206\u5173\u6ce8\u751f\u7269\u5927\u5206\u5b50\u3002\u4ed6\u505a\u7406\u8bba\u65f6\u5fc3\u91cc\u60f3\u7740\u7684\u5e94\u7528\u662f\u751f\u7269\u5927\u5206\u5b50\u3002 \u4fc4\u7f57\u65af\u4eba\u7684\u8bba\u6587\u6709\u4e00\u4e2a\u7279\u70b9\uff0c\u5c31\u662f\u5341\u5206\u6ce8\u610f\u7a81\u51fa\u4fc4\u56fd\u79d1\u5b66\u5bb6\u5728\u4e16\u754c\u79d1\u5b66\u53d1\u5c55\u4e2d\u7684\u8d21\u732e\u3002\u4f8b\u5982\uff0c\u9ad8\u5206\u5b50\u4ea4\u8054\u7f51\u7edc\u7684\u6eb6\u80c0\u70ed\u529b\u5b66\u7684Flory-Rehner\u7406\u8bba\uff0c\u4f1a\u6539\u4e3aFrenkel-Flory-Rehner\u7406\u8bba\u3002Volkenstein\u5728\u8c08\u5230de Gennes\u7684\u6807\u5ea6\u7406\u8bba\u65f6\uff0c\u4e5f\u63d0\u5230\u4e86I.\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":9191,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9191","url_meta":{"origin":9238,"position":4},"title":"Flory\u7684\u201c\u53e6\u4e00\u672c\u4e66\u201d","author":"Andrew","date":"2025\u5e744\u670820\u65e5","format":false,"excerpt":"\u67d0\u6821\u300a\u9ad8\u5206\u5b50\u7269\u7406\u300b\u8bfe\u671f\u672b\u8003\u8bd5\u7684\u201c\u82f1\u6587\u540d\u8bcd\u89e3\u91ca\u201d\u9898\u4e2d\uff0c\u8003\u5230\u201crotational isomeric state\u201d\uff08\u65cb\u8f6c\u5f02\u6784\u6001\uff09\u8fd9\u4e2a\u672f\u8bed\u3002\u6211\u611f\u5230\u5f88\u56f0\u60d1\u3002\u56e0\u4e3a\u8fd9\u4e2a\u672f\u8bed\u662f\u6bd4\u8f83\u6df1\u7684\u3002\u6211\u4eec\u6240\u91c7\u7528\u7684\u672c\u79d1\u9ad8\u5206\u5b50\u7269\u7406\u6559\u6750\uff0c\u6839\u672c\u6ca1\u6709\u6d89\u53ca\u5230\u8fd9\u4e2a\u6982\u5ff5\u3002\u8fd9\u4e2a\u6982\u5ff5\u751a\u81f3\u6ca1\u6709\u51fa\u73b0\u5728P. J. Flory\u7684\u201c\u90a3\u672c\u4e66\u201d\u2014\u2014Principles of Polymer Chemistry\u4e2d\uff08\u51fa\u7248\u4e8e1953\u5e74\uff09\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u6982\u5ff5\u662f\u7531\u041c\u0438\u0445\u0430\u0438\u0301\u043b \u0412\u043b\u0430\u0434\u0438\u0301\u043c\u0438\u0440\u043e\u0432\u0438\u0447 \u0412\u043e\u043b\u044c\u043a\u0435\u043d\u0448\u0442\u0435\u0301\u0439\u043d\uff08M. V. Volkenstein\uff09\u57281959\u5e74\u53d1\u8868\u7684\u8457\u4f5c\u041a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u044f \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0430 \u043f\u043e\u043b\u0438\u043c\u0435\u0440\u043d\u044b\u0445 \u0446\u0435\u043f\u0435\u0439\uff08\u805a\u5408\u7269\u94fe\u7684\u6784\u8c61\u7edf\u8ba1\uff09\u4e2d\u6b63\u5f0f\u63d0\u51fa\u7684\u30021963\u5e74\uff0c\u8be5\u4e66\u7684\u82f1\u6587\u7ffb\u8bd1\u5728\u7f8e\u56fd\u51fa\u7248\uff0cP. J. Flory\u5728\u5e8f\u4e2d\u9ad8\u5ea6\u8d5e\u8d4f\u4e86\u8be5\u8457\u4f5c\u3002\u540e\u8005\u7684\u201c\u53e6\u4e00\u672c\u4e66\u201d\u2014\u2014Statistical Mechanics of Chain Molecules\u4e5f\u4e8e1969\u5e74\u51fa\u7248\uff0c\u4f7f\u5f97\u65cb\u8f6c\u5f02\u6784\u6001\u2014\u2014\u8ba1\u7b97\u771f\u5b9e\u805a\u5408\u7269\u94fe\u7edf\u8ba1\u6027\u8d28\u7684\u4e00\u79cd\u8fd1\u4f3c\u601d\u60f3\u2014\u2014\u5f97\u5230\u66f4\u52a0\u4e3a\u4eba\u6240\u77e5\uff08\u5c3d\u7ba1\u8fd9\u672c\u4e66\u4ecd\u7136\u662f\u5c11\u6709\u4eba\u9605\u8bfb\u7684\uff09\u3002 M. Volkenstein\u539f\u8457\u5c01\u9762 \u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\uff0c\u4f7f\u5f97\u63cf\u8ff0\u771f\u5b9e\u94fe\u7684\u5316\u5b66\u952e\u8282\u590d\u6742\u6027\u2014\u2014\u4f8b\u5982\u4e0d\u5bf9\u79f0\u4ee5\u53ca\u5404\u81ea\u4e0d\u72ec\u7acb\u7684\u952e\u8282\u65cb\u8f6c\u52bf\u80fd\u66f2\u7ebf\u2014\u2014\u6709\u4e86\u53ef\u5199\u4e0b\u7684\u7edf\u4e00\u6570\u5b66\u5f62\u5f0f\u3002\u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770b\uff0c\u8fd9\u4e00\u5047\u8bbe\u9020\u6210\u7684\u597d\u5904\u662f\u6570\u5b66\u63cf\u8ff0\u7684\u79bb\u6563\u5316\u3002\u8fd9\u5f88\u50cf\u7531\u201c\u968f\u673a\u8fc7\u7a0b\u201d\u5230\u201c\u65f6\u95f4\u5e8f\u5217\u201d\u7684\u53d8\u5316\u65b9\u5f0f\u3002 \u4e0a\u4e16\u7eaa60\u5e74\u4ee3\u6070\u597d\u662f\u7535\u5b50\u8ba1\u7b97\u673a\u95ee\u4e16\u7684\u65f6\u4ee3\u3002\u590d\u6742\u7684\u8ba1\u7b97\u5982\u679c\u53ef\u4ee5\u88ab\u4ee5\u4e00\u79cd\u79bb\u6563\u5316\u7684\u65b9\u5f0f\u63cf\u8ff0\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u7535\u5b50\u8ba1\u7b97\u673a\u6765\u89e3\u51b3\u3002\u57fa\u4e8e\u77e9\u9635\u8fd0\u7b97\u7684\u7ebf\u6027\u4ee3\u6570\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u53d1\u6325\u4e86\u91cd\u8981\u7684\u4f5c\u7528\u3002\u6bd4\u5982\uff0c\u4ee5\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u4e3a\u6a21\u578b\u7684\u9884\u6d4b\uff0c\u5176\u5b9e\u662f\u843d\u5b9e\u5230\u8f6c\u79fb\u77e9\u9635\u7684\u8fd0\u7b97\u4e0a\u3002\u540c\u7406\uff0c\u57fa\u4e8e\u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\u5bf9\u771f\u5b9e\u94fe\u8fdb\u884c\u79bb\u6563\u5316\u63cf\u8ff0\u540e\uff0c\u6709\u671b\u901a\u8fc7\u8ba1\u7b97\u673a\uff0c\u7ed9\u5b9a\u5316\u5b66\u5f0f\uff0c\u9884\u6d4b\u51fa\u94fe\u7edf\u8ba1\u7ed3\u679c\u2014\u2014\u8fd9\u5c06\u8fdb\u4e00\u6b65\u7528\u4e8e\u9884\u6d4b\u805a\u5408\u7269\u6750\u6599\u7684\u8bb8\u591a\u6027\u8d28\u3002\u8fd9\u65e0\u7591\u662f\u4ee4\u4eba\u5174\u594b\u7684\u3002\u4f46\u662f\u4f5c\u4e3a\u4e00\u95e8\u79d1\u5b66\uff0c\u8fd9\u4e00\u5047\u8bbe\u662f\u5426\u7b26\u5408\u5b9e\u9645\uff0c\u9700\u8981\u5b9e\u9a8c\u9a8c\u8bc1\u3002\u800c\u5b9e\u9a8c\u7684\u53ef\u9a8c\u8bc1\u6027\u7406\u8bba\uff0c\u662f\u4efb\u4f55\u4e00\u9879\u7406\u8bba\u5de5\u4f5c\u7684\u201c\u53e6\u591650%\u52aa\u529b\u201d\u3002Volkenstein\u539f\u4e66\u603b\u7ed3\u4e86\u5927\u91cf\u53ef\u80fd\u7528\u4e8e\u9a8c\u8bc1\u8fd9\u4e00\u7406\u8bba\u7684\u5b9e\u9a8c\u65b9\u6cd5\u2014\u2014\u5305\u62ec\u5076\u6781\u77e9\u6d4b\u91cf\u3001\u5149\u6563\u5c04\u3001Kerr\u6548\u5e94\u7b49\u3002\u4f46\u662f\u8fd9\u4e9b\u5b9e\u9a8c\u65b9\u6cd5\u4e0e\u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\u6b63\u786e\u6027\u7684\u8054\u7cfb\uff0c\u4f9d\u7136\u85cf\u5728\u590d\u6742\u800c\u95f4\u63a5\u7684\u6570\u91cf\u5173\u7cfb\u4ee5\u53ca\u66f4\u591a\u5b9e\u9a8c\u5047\u5b9a\uff08\u6bd4\u5982valence-optical scheme\uff09\u4e4b\u4e0b\u3002 \u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770b\uff0c\u9ad8\u5206\u5b50\u7269\u7406\u7406\u8bba\u7684\u53d1\u5c55\u4e0e\u6db2\u4f53\u7269\u7406\u7684\u53d1\u5c55\u82e5\u4e0d\u80fd\u8bf4\u662f\u540c\u65f6\u7684\uff0c\u5219\u524d\u8005\u751a\u81f3\u8d85\u524d\u4e8e\u540e\u8005\u3002\u56e0\u6b64\uff0c\u6210\u529f\u7684\u9ad8\u5206\u5b50\u7269\u7406\u5b66\u5bb6\uff0c\u514d\u4e0d\u4e86\u8981\u5728\u6db2\u4f53\u7269\u7406\u95ee\u9898\u4e0a\u6709\u5148\u950b\u5f0f\u7684\u6b63\u786e\u8ba4\u8bc6\u3002\u8fd9\u5728Flory\u7684Principles in Polymer Chemistry\u4e00\u4e66\u4e2d\u662f\u6709\u6240\u4f53\u73b0\u7684\u3002\u4f8b\u5982\u5728\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7edf\u8ba1\u90e8\u5206\uff0cFlory\u201c\u5570\u55e6\u201d\u4e86\u4e00\u6bb5\u8bdd\uff08p. 497 sec. 1a\u7684\u7b2c2\u81ea\u7136\u6bb5\uff09\uff0c\u5b9e\u9645\u4e0a\u9053\u51fa\u4e86\u6db2\u4f53\u7684\u5f84\u5411\u5206\u5e03\u51fd\u6570\u6982\u5ff5\uff01\u53cd\u4e4b\uff0cVolkenstein\u7684\u539f\u4e66\uff0c\u53cd\u6620\u4e86\u524d\u82cf\u8054\u79d1\u5b66\u5bb6\u5728\u0412\u0430\u043b\u0435\u043d\u0442\u0438\u043d \u0410\u043b\u0435\u043a\u0441\u0435\u0435\u0432\u0438\u0447 \u041a\u0430\u0440\u0433\u0438\u043d\uff08V. A. Kargin\uff09\u5173\u4e8e\u6db2\u6001\u7684\u843d\u540e\u8ba4\u8bc6\u7684\u5f71\u54cd\u3002\u5728Kargin\u5f53\u9886\u5bfc\u7684\u671f\u95f4\uff0c\u8fd9\u4e9b\u89c2\u70b9\u662f\u7528\u6765\u5bf9\u6297\u6765\u81ea\u7f8e\u56fd\u540c\u884c\u7684\u4e0d\u540c\u89c2\u70b9\u7684\u3002\u0418\u043b\u044c\u044f\u0301 \u041c\u0438\u0445\u0430\u0301\u0439\u043b\u043e\u0432\u0438\u0447 \u041b\u0438\u0301\u0444\u0448\u0438\u0446\uff08I. M. Lifshitz\uff09\u7684\u66f4\u52a0\u6b63\u786e\u7684\u9ad8\u5206\u5b50\u7269\u7406\u89c2\u70b9\uff081968\u5e74\uff09\u88ab\u63a8\u8fdf\u5230\u65af\u5927\u6797\u65f6\u4ee3\u4e4b\u540e\u624d\u4e3a\u4eba\u6240\u77e5\u3002\u56e0\u6b64\uff0c\u4eca\u5929\u518d\u60f3\u4e86\u89e3\u8fd9\u90e8\u5206\u5185\u5bb9\uff0c\u5e94\u8be5\u76f4\u63a5\u770bFlory\u7684\u8457\u4f5c\u3002Flory\u7684\u8457\u4f5c\u5305\u62ec\u4e86\u4ed6\u672c\u4eba\u548c\u540e\u671f\u7684\u51e0\u4e2a\u540c\u4e8b\u548c\u5b66\u751f\uff1aJ. Mark\u3001A. Abe\u3001R. Jernigan\u3001A. Tonelli\u7684\u540e\u7eed\u5de5\u4f5c\uff1b\u4ed6\u4eec\u53d1\u8868\u4e86\u540c\u4e00\u7269\u7406\u91cf\u7684\u7406\u8bba\u8ba1\u7b97\u548c\u5b9e\u9a8c\u6d4b\u91cf\u7ed3\u679c\u6bd4\u8f83\uff0c\u5341\u5206\u5b8c\u7f8e\u7684\u5370\u8bc1\u4e86Volkenstein\u94fe\u7edf\u8ba1\u7406\u8bba\u7684\u6210\u529f\uff0c\u6bd4\u5982\u4ee5\u4e0b\u8457\u540d\u63d2\u56fe\u3002 \u7528Monte Carlo\u6a21\u62df\u751f\u6210\u7684\u7acb\u4f53\u5f02\u6784\u65e0\u89c4\u94fe\u7279\u5f81\u6bd4\uff0c\u4e0e\u7406\u8bba\u8ba1\u7b97\u7279\u5f81\u6bd4\u7684\u6bd4\u8f83\u56fe","rel":"","context":"In &quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":9332,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9332","url_meta":{"origin":9238,"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 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